the turing machine as a tool for dynamic modeling 2

04/03/2012 C.G[Texte]

THE TURING MACHINE AS A TOOL FOR DYNAMIC MODELING ............................... 2

1.B PRESENTATION .......................................................................................................... 3

2.B APPROACH .................................................................................................................... 3

2.B 1 DESCRIPTION OF THE APPROACH ....................................................... 4

2.B 2 THE IMAGE OF THE PHENOMENON OBSERVED ................................ 5

2.B 3 GRID ANALYSIS ........................................................................................ 7

2.B 4 TABLE FOR THE IDENTIFICATION AND CREATION OF THE OPERATOR ...................................................................................................... 12

2.B 5 RESEARCH GROUP ............................................................................... 14

3.B0 LES APPRENTISSAGES ........................................................................................... 15

3.B2 OPERATEUR IG ........................................................................................................ 16

Analysis grid ...................................................................................................... 16

Description of the functioning of the IG operator ............................................... 17

Statement of changes ........................................................................................ 20

Grouping together.............................................................................................. 25

Identification table.............................................................................................. 26

Généralisation des positions ............................................................................. 27

Cross-checking .................................................................................................. 28

Opérator IG ....................................................................................................... 29

3.B3 OPERATOR GG ......................................................................................................... 30

Analysis grid ...................................................................................................... 30

Description of the operator GG .......................................................................... 31

Statement of changes ........................................................................................ 33

Grouping together.............................................................................................. 38

Identification table.............................................................................................. 39

Généralisation des positions ............................................................................. 40

Cross-checking .................................................................................................. 41

Opérator GG ...................................................................................................... 41

3.B4 GROUP SUBSTITUTION .......................................................................................... 42

Analysis grid .................................................................................................... 42

Description of the functioning the operator DE ............................................ 44

Statement of changes ..................................................................................... 46

Grouping together ........................................................................................... 51

Identification table ........................................................................................... 52

Généralisation des positions ......................................................................... 53

Cross-checking................................................................................................ 54

Opérateur DE {BC->CB} .................................................................................. 55

04/03/2012 C.G[Texte]

Application of the operator DE {BC - CB} to text DO2 ................................. 56

3.B5 BINARY DIGITAL ADDITION ................................................................................ 59

Analysis grid ...................................................................................................... 60

binary digital addition analysis ........................................................................... 60

Grouping ............................................................................................................ 66

Table d’identification .......................................................................................... 68

Généralisazion .................................................................................................. 69

Aggregation ...................................................................................................... 70

Opérateur AN( réduit ) ....................................................................................... 70

Application of a digital binary addition operator(AN) .......................................... 72

3.B6 AUTOMATON ........................................................................................................... 77

Analysis grid ...................................................................................................... 78

Relevé des changements observés................................................................... 80

Grouping ............................................................................................................ 81

Table d’identification .......................................................................................... 82

Généralisazion - Aggréga .................................................................................. 83

Opérator AU ..................................................................................................... 83

7.B 1 REMINDER ............................................................................................................... 84

8.B1 BIBLIOGRAPHIE ....................................................................................................... 85

04/03/2012 C.G[Texte]

THE TURING MACHINE AS A TOOL FOR DYNAMIC MODELING

1.B PRESENTATION

Informations gathered by the observation of various events are subject to the analysis of a

grid, built on the principle of the functioning of the Turing machine playing the role of an

observer

It is based on the use of States linking several elements: nature of the acquired information,

position, movement. This state induced changes on these elements as well as the State itself.

Registration of changes with this method allows to reproduce and build a model independent

approach of observed phenomena and follow their evolution.

The form in which the collected information are encoded is free: numeral, letters, icons,

tableau…... They are arranged on an image which reflects the progress of the observed

changes

The grid takes these elements, connects them by States, the flow thus describing the observed

phenomenon. These elements are grouped together forming tables with which the phenomena

are identified.

By successive learning and intersections between these various observations, an operator is

gradually built that reproduces these observations to simulate them and allow new action

(research of route, of ordered group, successive transformations of signs …).

2.B APPROACH

The course of this analysis includes first seizure of a picture of the changes from the

information transmitted by the outside environment. This image is then taken over by a grid

that connects the events observed by States. Obtained tables are immediate guides which

reproduce the sequence of events. Their registration as States makes possible a generalization

of the procedures used. The creation of operators by learning broadens the scope beyond a

simple imitation.

The tables also allow internal research for recognition or reconstitution of all suites sign

(words, new routes, earlier steps...). These results are made available through the tissues of

links between events made available in these tables by the use of the analysis grid.

04/03/2012 C.G[Texte]

2.B 1 DESCRIPTION OF THE APPROACH

The observation of events accompanying the conduct of a phenomenon allows to inform an

image. This image is analyzed using a grid built on the principle of operation of a Turing

Machine. It gets so by successive learning a model of a shape analogous to the structure of the

grid. This result is an operator that simulates the phenomenon observed by applying it to a

field of data consistent with those used for this analysis.

The observed events are coded by a sign associated with its position on the image. The Group

of the signs used in this case sets the scope of the operator. An observed phenomenon may

represent thus:

n1..........^

LN1 : [] 1 0 1 1

n2................... ^

LN2 : [] 0 0 0 0

It is reset to a group of signs and placement of the index on the final position of a scanning

from left to right.

LN1 is the initial situation and LN2 the situation after the action of an operator

The signs are figures, icons, letters, sign group. Some signs have a cutoff point (spacing

white…) meaning

The domain of this operator includes the signs 1 and 0 and with regard to the cuts, spacing [].

It is specific to this area.

The image is a representation of the observed phenomenon. For each event it indicates the

sign of origin, its transformation and its new position if applicable. These signs are divided on

different tracks according to their nature (origin, result, incident)

The image is analyzed using common to all the analysis grid. The structure of this grid is

fixed and independent of the observed phenomenon.

The sequence of events from this observation has a name defined by the user with a reference

to the step current AN.1, GG.4 ……

The grid associated with each row of the image a State specific GXS, GX€, GX£ and the

successive transformations of these States from one line to another.

The LN2 line gives the result of these changes as is found on the image, representation of the

phenomenon itself. The suite of States reports these findings not related to the operation that

produced this result.The result LN2 line gives the culmination of these transformations as is

04/03/2012 C.G[Texte]

found on the image, representation of the phenomenon itself. The suite of States reports these

findings not related to the operation that produced this result.

These different stages of the analysis are grouped by ordering them around the States that

have marked the stages of this work. They form identification tables that allow to find

sequences of signs as the words of a text using a lexicon or search journeys on a group of

routes or a built map with grid.

These tables are progressively supplemented by successive learning. Crosschecking between

collected items, have built the operator which reproduces the comments now forming an

internal representation of the observed phenomenon.

These tables can also recognize already existing operators when using the operators

themselves as the object of analysis and overlap them.

2.B 2 THE IMAGE OF THE PHENOMENON OBSERVED

The images show the events identified in the observation of a phenomenon. This observation

is divided into stages corresponding to the various stages of the analysis of the grid indicated

by the movement of the index. Each step is described by 4 successive stages identified by the

grid lines.

The events are described by signs (letter, number, number, icon) and a position relative to the

previous image. The Group of the signs used in this case sets the scope of the operator.

The images are structured in three-way

LX1 events "origin"

LX2 for the result of the changes observed

LX ° where intermediate events alter the result

The positions of the relevant elements are indicated by the index on n1, n2, and n°.

n2 : ^

LX2 : 0 0 1 1 1 []

n° : ^

LX° : []

n 1 : ^

LX1 : 0 0 1 1 1 []

By hypothesis, the initial position of a positive reading of left to right 1 (negative and 0 in the

reverse direction)

In the image below, representative of a simple movement of the index, the signs listed subject

to operator LN events remain the same between origin and outcome. Their positions are

successively swept away, step by step.

The positioning of the index to the right end of LN2 is the result of this operation (in the case

of a stop on a spacing and regression of a position). This last line LN2, is the result of the

action of the operator LN line and can be used by a new operator origin

04/03/2012 C.G[Texte]

n2 : ^

LN2: 0 0 1 1 1 []

n° : ^

LN° : [] []

n 1 ^

LN° : 0 0 1 1 1 []

These lines LX names are modified based on the operators to which they are attached. LN1,

LN °, LN2, in this case LN operator. This convention is used to facilitate the effort of

memorization, however the names remain free.

In the case of a binary numerical addition (AN operator).

n2 : ^

AN2 : b 1 1 0 0 0

n° : ^

AN° : b b 1 0 1 1

n1 : ^

AN1 : b b 1 1 0 1

AN1 supports the first argument of 1 addition and AN ° the second 1. The result of this first

addition is indicated 0 on AN2.

In some cases as a path of route identified simply by steps A, B, D,..., the IT1 line is only

concerned

n2 : ^

IT2 : []

n° : ^

IT° : []

n1 : ^

IT1 : A B D F E

In the case of an automaton, line 1 is filled successively the changes on the States of the

automaton events encountered running and mentioned on AN °.

A->a->D->e->A->b->C->d

n2 : ^

AU2 : []

n° : ^

AU° : a e b d

n1 : ^

AU1 : A D A C D

The image representing the phenomenon observed changes, is then studied by the analysis

grid to construct an operator whose actions reproduce these changes.

04/03/2012 C.G[Texte]

2.B 3 GRID ANALYSIS

This grid is used during the period of observation of a phenomenon to record the events

recorded in the image of this phenomenon and to order them. This work will build an operator

who then models the observed changes and their dynamics. By this approach, provides

identification, simulation and forecasting tool built on the same pattern of operation.

As in the Turing Machine, this grid is based on the use of States relating within the same

entity observed events and their linking.

The elements of the grid are related successively to the three lines of the image.

LX1

The index i must be read as if (sign of E on LX1)

LX°

The index j must be read as €j (sign of E on LX °)

LX2

The k index must be read as £ k (sign of E on LX2)

The LX lines under the control of the GX States are affected (p) index used in the event of

contradiction in the course of the analysis. In this case, assumes that a previous event caused a

change in the GX which justifies this new trend. This change is indicated by a change in the

index (p) in the States. The cases examined limit this index to simple variations. This rule of

non-contradiction is the basis for the operation of the grid

Each line contains various headings common to the three LX1, LX °, LX2 lines but the

actions differ according to the lines and the values of the signs.

G.E Q ST IMG N D E A E’ IMG N D DC Q'

GXS(p) Si LX1 n1 +/- Si -> GXS(p)i

GXS(p)i Si LX1 n1 0 Si -> GX€(p)i


GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij


GX£(p)i[] £k LX2 n2 +/- £k r/w £k LX2 n2 +/- GXS(p)

[ ] LX2 n2 +/- [ ] -> GXS(p)

GX£(p)ij £k LX2 n2 +/- £k r/w £k LX2 n2 +/- GXS(p)

[ ] LX2 n2 +/- [ ] -> GXS(p)

04/03/2012 C.G[Texte]

-G.E. refers to the sequence of events during analysis and indicates the step

where the course of the analysis

IDA.2 refers to the suite 0 0 1 1 1[] and step 2 in the following IDA

n2 : ^

LX1: 0 0 1 1 1 []

For the LX1 line

-Q State of this line assigned with index (p): IDS (1)

-ST index constituted by the observed E event: 0

-IMG line of the image where the work in progress: LX1

- N the coordinate system of the event on the studied line: 2

-D displacement on the image for the following reading: + 1

-E reminder of the code of the event already used as an index of State IDS: 0

The Middle figure, A action carried out under this State by the grid to the LX1 line is

formed by:

-> Transfer in a State identical to the original line but noted with the value of E


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0


IDA.2 IDS(1) 0 LX1 2 +1 0 -> IDS(1)0

04/03/2012 C.G[Texte]

and

-> The State IDS (1) 0 linked to the LX1 line causes a transfer on the LX ° line

under the State ID€ (1) 0 with no change in position D = 0, index p(1) and index i= 0

For the LX ° line

The LX ° line is complementary events amending the code or the position of the original

event.

It has the same topics: G.E, Q, ST, IMG, N, D

Action A consists of a transfer of GX€(p) i to GX£ enriched index j met on the GX€(p)ij line

or white space GX€ (p) i [] otherwise. The index j must be read as €j

For the LX2 line

It has the same topics: G.E., Q, ST, IMG, N, D, E

As a general rule, we encounter as action [r/w] printing of a sign on the line and at the

indicated position and transfer on a new initial state

This sign was read on the line and at the position indicated in the analysis phase. It is a copy

registered and copied by the grid back

In the case of a route, the grid saves without printing this step which gives rise to a change of

position of reading but no transformation of the signs read.

The stage ends with a return to the GXS (p) State line LX1.

Where by the grid of inconsistency with a previous step, back on the first line read

corresponding to elements with a contradiction.

First reading

Detection by the grid of an anomaly in position N =-3 and return to the first line of origin of

the anomaly N = 0


IDA.2 IDS(1)0 0 LX1 3 0 0 -> ID€(1)0


GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij


IDA.1 ID£(1)0[] 0 LX2 1 +1 0 r/w 0 LX2 1 +1 IDS(1)

AN£1)11 0 LN2 0 -1 0 w 0 LN2 0 -1 ANS(1)

AN£1)11 1 LN2 -3 -1 1 x 1 LN2 -3 -1 ANS(1)

04/03/2012 C.G[Texte]

Modification of index p on the first line

And resumption of analysis from the first line

The end of the execution of an operator is reported by [!] followed by DC (+/-) to take into

account the following operator, if applicable The end of the execution of an operator is

reported by [!] followed by DC (+/-) to take into account the following operator, if applicable

The last DC encountered topic relates to the linking of the operator running with the

following. When it encounters the repetition of an operator, it can be indicated by the sign (: |)

Group substitution

The change may concern several signs simultaneously. Bold is used to identify these groups,

ABCDE ->ACBHDE

This hypothesis is taken into account by the grid in this form

The reading of a character fat resulted in a transfer of GXS (p) in GXS (p) i (i bold). The

character read after moving +/-1 perhaps also fatty into GX€ (p) i or not and then found a

normal index GX€ (p) i.

There is a similar level of LX2 conduct and k index (£ k)

f/b 1 LN1 0 -1 ANS(1)

AN£1)11 0 LN2 0 -1 0 -> 0 LN2 0 -1 ANS(2)

GXS.cc2 ! +/-



Si LX1 n1 +/- Si -> GXS(p)i

GXS(p)i Si/Si LX1 n1 0 Si/Si -> GX€(p)i



GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)

04/03/2012 C.G[Texte]

When the grid meets these character groupings, it reads all the fatty signs concerned and

performs the transformation that overall which allows to take into account different size

groups.

Les signes de séparation

White spaces are used where one distinguishes the meaning of the displacement of the

scanning: [+] from left to right and [-] in the opposite direction.

It also uses of slashes to indicate and consider the separation of the [/] words in a text



£k LX2 n2 +/- £k w £k LX2 n2 +/- GX£(p)ik

[ ] LX2 n2 +/- [ ] -> GXS(p)

GX£(p)ik £r LX2 n2 +/- £r w £r LX2 n2 +/- GX£p)ik

£r LX2 n2 +/- £r r/w £r LX2 n2 +/- GXS(p)


GXS.cc1 Si LX1 n1 0 Si -> GXS(p)

Si LX1 n1 0 Si -> GXS(p)

[] LX1 n1 0 [] -> GXS.cc2

GXS.cc2 ! +

GXS.cc3 [/] LX1 n1 +1 [/] -> GX€.cc3

GX€.cc3 [ ] LX° n° +1 [ ] -> GX£.cc3

GX£.cc3 [ ] LX2 n2 +1 [ ] -> GXS.cc2

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

04/03/2012 C.G[Texte]

For each identified by its sign delimiter, the table above gives the procedure to be adopted

Internal actions by the grid

Is explicitly not the diverse actions necessary to the loading of the image and the formatting

of these data to inform the grid lines

The actions « A » in the grid are :

- [->] States transfers GXS-> GXS (p) i-> GX€ (p) i-> RI £ (p) ij associated with the

transfer of lines corresponding LX1, LX °, LX2

-[r/w] reading - printing of the data on the row LX2

-[x] stopping of the analysis in the event of contradiction on LX2

-[f/b] Search and return to the origin of the LX1 contradiction step

2.B 4 TABLE FOR THE IDENTIFICATION AND CREATION OF THE OPERATOR

This table is the result of the consolidation of lines made at the end of the analysis of the

image by the grid around the various States involved in this operation as in learning (IG)

IGA.1 IGS(1) 1 LN1 0 -1 1 -> IGS(1)1

IGA.2 IGS(1) 1 LN1 -1 -1 1 -> IGS(1)1

IGA.3 IGS(1) 1 LN1 -2 -1 1 -> IGS(1)1

IGA.4 IGS(1) 1 LN1 -3 -1 1 -> IGS(1)1

IGA.5 IGS(1) 0 LN1 -4 -1 0 -> IGS(1)0

IGA.6 IGS(1) [-] LN1 -5 - 0 [-] -> IGS.cc5

IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1

IGA.2 IGS(1)1 1 LN1 -2 0 1 -> IG€(1)1

IGA.3 IGS(1)1 1 LN1 -3 0 1 -> IG€(1)1

IGA.4 IGS(1)1 1 LN1 -4 0 1 -> IG€(1)1

IGA.5 IGS(1)0 [ ] LN1 -5 0 [ ] -> IG€(1)0

IGA.1 IG€(1)1 [ ] LN° 0 -1 [ ] -> IG£(1)1[]

IGA.2 IG€(1)1 [ ] LN° -1 -1 [ ] -> IG£(1)1[]

IGA.3 IG€(1)1 [ ] LN° -2 -1 [ ] -> IG£(1)1[]

IGA.4 IG€(1)1 [ ] LN° -3 -1 [ ] -> IG£(1)1[]

IGA.5 IG€(p)0 [ ] LN° -4 -1 [ ] -> IG£(1)0[]

IGA.1 IG£(1)1[] 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)

IGA.2 IG£(1)1[] 1 LN2 -1 -1 1 r/w 1 LN2 -1 -1 IGS(1)

IGA.3 IG£(1)1[] 1 LN2 -2 -1 1 r/w 1 LN2 -2 -1 IGS(1)

04/03/2012 C.G[Texte]

This table can be generalized by replacing the absolute addresses contained therein relating

addresses used in the model of the grid. In this case, the lines can be reduced by intersection

IGA.4 IG£(1)1[] 1 LN2 -3 -1 1 r/w 1 LN2 -3 -1 IGS(1)

IGA.5 IG£(1)0[] 0 LN2 -4 -1 0 r/w 0 LN2 -4 -1 IGS(1)

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

IGS.cc2 ! +

IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGS(1) 0 LN1 n1 -1 0 -> IGS(1)0

IGS(1) [-] LN1 n1 - 0 [-] -> IGS.cc5

IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGS(1)0 [ ] LN1 n1 0 [ ] -> IG€(1)0

IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IG€(1)0 [ ] LN° n° -1 [ ] -> IG£(1)0[]

IG£(1)1[] 1 LN2 n2 -1 1 r/w 1 LN2 n2 -1 IGS(1)

IG£(1)0[] 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 IGS(1)

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

04/03/2012 C.G[Texte]

From this reduction, these data are taken back to form the operator

Full operator is obtained by learning to progressive analyze all the possible cases

2.B 5 RESEARCH GROUP

(cf. les applications 4.1, 4.3, 4.5)

Tables of identification obtained by analysis can be used to search for and identify

groups of signs through the actions of comparison available on the grid. This type of

recognition is limited to simple cases and is based on the use of internal functions to

the grid.

- New routes are chosen on a set of available routes

The group is defined by an origin sign and a terminal sign. The suite of the retained

signs depends on used identification table which is swept with associations that it

proposes.

-Word identification on a text

In this case, not only the first sign and the last are but also imposed then ordered the

rest of the group. . To achieve this result, it is first necessary to submit the text cutting

IGS.cc2 ! +

IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

0 LN1 n1 -1 0 -> IGS(1)0

[-] LN1 n1 0 [-] -> IGS.cc5

IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGS(1)0 [ ] LN1 n1 0 [ ] -> IG€(1)0

IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IG€(1)0 [ ] LN° n° -1 [ ] -> IG£(1)0[]

IG£(1)1[] 1 LN2 n2 -1 1 r/w 1 LN2 n2 -1 IGS(1)

IG£(1)0[] 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 IGS(1)

IGS.cc5 [-] LX1 n1 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° n° +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 n2 +1 [-] -> IGS.cc2

IGS.cc2 ! +

04/03/2012 C.G[Texte]

analysis and closer to each of the lines obtained from those of the already developed

lexicon. It meets usually several lines responding positively to this comparison. The

identification is dropdown concatenation proposed by analysis. In the event of

contradiction, the grid uses cut and recovery actions previously encountered

-Opérator identification

This identification can be for identical areas of sign. All of the operators concerned

are brought together in a table of common identification. Step by step, the observed

analysis lines are compared with the corresponding lines of the operators considered

by this table. By successive elimination, among the operators proposed the same field

of sign, the operator with an identical action process will be selected if there is

otherwise a new operator is created.

3.B0 LES APPRENTISSAGES

IG- Movement of the index at the left end of a group of signs without processing signs

[] 1 1 1 1 -> [] 1 1 1 1

ID --Movement of the index without processing on the last character right of a suite of signs.

0 0 1 1 1 [ ] -> 0 0 1 1 1 [ ]

DE -Substitution of a new group of variable to a former group also length of variable-length

characters

ABCDE ->ACBHDE

Groups are designated by the bold which constitute

AN -A from of an image representing the two arguments and the result to obtain, are analyzed

using a grid and an independent process observable changes from an external point of view.

bb1101+ bb1011 -> b11000

AU -All the States setting an Automat is obtained by the following concatenation and

competing events survey observed

A->a->D->e->A->b->C->d

where the transformation of A State is defined by the event met with "a". The State resulting

from D in the presence of "e" transforms himself into A………

04/03/2012 C.G[Texte]

3.B2 OPERATEUR IG

Movement of the index at the left end of a group of signs without processing signs

^ ^

[] 1 1 1 1 -> [] 1 1 1 1

Analysis grid



SI LX1 n1 +/- SI -> GXS(p)i

[+] LX1 n1 0 [+] -> GXS.cc4

[-] LX1 n1 0 [-] -> GXS.cc5

[/] LX1 n1 0 [/] GXS.cc3




GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)




[ ] LX2 n2 +/- [ ] -> GXS(p)


£k LX2 n2 +/- £k r/w £k LX2 n2 +/- GXS(p)


04/03/2012 C.G[Texte]

Description of the functioning of the IG operator

The domain in which this operator IG includes signs 1 and 0 and, with regard to the cuts,

spacing [].

The observed phenomenon is thus:

n2.........................^

LN2 : 0 1 1 1 1

n°.........................^

LN°.....................[]

n 1........................^

LN1 : 0 1 1 1 1

^

IGA refers to signs subject of this analysis group 0 1 1 1 1. IGA.1, IGA.2.... .are the

successive stages of the review.

^

[ ] LX2 n2 +/- [ ] -> GXS(p)




[] LX1 n1 0 [] -> GXS.cc2

GXS.cc2 ! +

GXS.cc3 [/] GX1 n1 +1 [/] -> GX€.cc3

GX€.cc3 [ ] GX° n° +1 [ ] -> GX£.cc3

GX£.cc3 [ ] GX2 n2 +1 [ ] -> GXS.cc2

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

04/03/2012 C.G[Texte]

LN1 track gives the image of the original situation 01111, LN2 gives final without any

processing situation since it is a simple movement of the index.

In the absence of any intermediate track LN ° contains only spacing [].

The index position n1 = 0 LN1 originally of treatment towards moves by successive steps

IGA.1, IGA.2,... .to the signs located on its left in copying the same. Each step is running in

four phases.

n2.........................^

LN2 : 0 1 1 1 1

n°.........................^

LN°.....................[]

n 1........................^

LN1 : 0 1 1 1 1

In this first phase, the D index position 0 on LN1 is moved from –1 (negative since the

movement occurs from right to left). The IGS State (1) track LN1 is transformed in

{IGS (1)1}

n2........................^

LN2 : 0 1 1 1 1

n°.........................^

LN°.....................[]

n 1.....................^

LN1 : 0 1 1 1 1

In the same step IGA.1, movement is also reflected, in a second phase, on the way LN ° by a

transfer of the IGS State (1) 1 in IG€ (1) no new displacement in order to regain this position

of the scanning LN1 towards the next step.

n2........................^

LN4 : 0 1 1 1 1

n° :...................^

LN° :..................[]

n 1....................^

LN1 : 0 1 1 1 1

The absence of any character met at the level of the line LN ° allows an immediate transfer of

the State IG€ (1) 1 in IG£ (1)1[]



IGA.1 IGS(1) 1 LN1 0 -1 1 -> IGS(1)1


IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1

G.E Q ST IMG N D E Ô E IMG N D DC Q'

GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)i[]

IGA.1 IG€(1)1 [ ] LN° 0 -1 [ ] -> IG£(1)1[]

04/03/2012 C.G[Texte]

n2........................^

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]

n 1.................... ^..

LN1 : 0 1 1 1 1

In the last phase of this first stage, the r/w action fill character 1 already on LN2 position

n2 = - 1 to make the first result of the applied IG operator to the group 0 1 1 1 1.

The device is ready to perform a new step IGA.2.

When the reading of the Group of characters reaches its limits indicated by a blank spacing []

on the path of origin, grid transfers the IGS State (1) in IGS.cc5 (cf.grille). The operator stops

on the last position affected e.g. on the first position to the left of the signs concerned group.

n2.......... ^

LN2 : [] 0 1 1 1 1

n°...........^......

LN°.......[].......

n1 .........^

LN1 : [] 0 1 1 1 1

n2.......... ^

LN2 : [] 0 1 1 1 1

n°........... ^......

LN°.......[].......

n1 ......... ^

LN1 : [] 0 1 1 1 1

After the grouping of the various stages IGA.1, IGA.2.... that accompany the conduct of the

action of the operator IG, the States are assembled in the form of tables.

These tables are ordered by type of State corresponding to the various phases of analysis


GX£(p)i[] £k LN2 n2 +/- £k r/w £k LN2 n2 +/- GXS(p)

IGA.1 IG£(1)1[] 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)

GXS(p) [-] LX1 n1 -0 [-] -> GXS.cc5

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

IGA.6 IGS(1) [-] LN1 -5 -0 [-] r/w 0 LN2 n2 -1 IGS.cc5

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

04/03/2012 C.G[Texte]

IGS(1), IGS(1)1, IG€(1)1, IG£(1)1[]

By bringing the elements of this table of the result of an analysis of a new group, can identify

an identical operator or to list a new.

We can also generalize this table returning to the positions indicated that in the grid

Opérateur: IG

D : { 1,0 } { [] }

Statement of changes n2.........................^

LN4 : 0 1 1 1 1

n°.........................^

LN°.....................[]

n 1........................^

LN1 : 0 1 1 1 1

n2........................^

LN4 : 0 1 1 1 1

n° :...................^

LN° :..................[]

n 1....................^

LN1 : 0 1 1 1 1

n2........................^

LN4 : 0 1 1 1 1

n° :...................^

LN° :..................[]

n 1....................^

LN1 : 0 1 1 1 1

IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1

IGA.2 IGS(1)1 1 LN1 -2 0 1 -> IG€(1)1

IGA.3 IGS(1)1 1 LN1 -3 0 1 -> IG€(1)1


GXS(p) Si LN1 n1 -1 Si -> GXS(p)i

IGA.1 IGS(1) 1 LN1 0 -1 1 -> IGS(1)1


IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1


GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)i[]

IGA.1 IG€(1)1 [ ] LN° 0 -1 [ ] -> IG£(1)1[]

04/03/2012 C.G[Texte]

n2........................^

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]

n 1.................... ^..

LN1 : 0 1 1 1 1

n2......................^...

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]...

n 1....................^....

LN1 : 0 1 1 1 1

n2......................^...

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]...

n 1.................^....

LN1 : 0 1 1 1 1

n2......................^...

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]...

n 1.................^....

LN1 : 0 1 1 1 1

n2.....................^...

LN4 : 0 1 1 1 1

n° :............^...

LN° :...........[]...



IGA.1 IG£(1)1[] 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)


IGS(p) Si LN1 n1 -1 Si -> GXS(p)i

IGA.2 IGS(1) 1 LN1 -1 -1 1 IGS(1)1


IGA.2 IGS(1)1 1 LN1 -2 0 1 -> IG€(1)1


GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)i[]

IGA.2 IG€(1)1 [ ] LN° -1 -1 [ ] -> IG£(1)1[]

04/03/2012 C.G[Texte]

n 1.................^....

LN1 : 0 1 1 1 1

n2..................^

LN2 : 0 1 1 1 1

n°.................. ^...

LN°...............[]....

n1..................^

LN1 : 0 1 1 1 1

n2..................^

LN2 : 0 1 1 1 1

n°...................^......

LN°...............[].......

n1 ..............^

LN1 : 0 1 1 1 1

n2..................^

LN2 : 0 1 1 1 1

n°...................^......

LN°...............[].......

n1 ..............^

LN1 : 0 1 1 1 1

n2..................^

LN2 : 0 1 1 1 1

n°................^......

LN°............[].......

n1 ..............^

LN1 : 0 1 1 1 1


GX£(p)i[] £k LN2 n2 +/- £k -> £k LN2 n2 +/- GXS(p)

IGA.2 IG£(1)1[] 1 LN2 -1 -1 1 r/w 1 LN2 -1 -1 IGS(1)


GXS(p) Si LN1 n1 0 Si -> GXS(p)i

IGA.3 IGS(1) 1 LN1 -2 -1 1 -> IGS(1)1


IGA.3 IGS(1)1 1 LN1 -3 0 1 -> IG€(1)1


GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)i[]

IGA.3 IG€(1)1 [ ] LN° -2 -1 [ ] -> IG£(1)1[]


IGA.3 IG£(1)1[] 1 LN2 -2 -1 1 r/w 1 LN2 -2 -1 IGS(1)

04/03/2012 C.G[Texte]

n2................^

LN2 : 0 1 1 1 1

n°................^......

LN°............[].......

n1 ..............^

LN1 : 0 1 1 1 1

n2................^

LN2 : 0 1 1 1 1

n°................^......

LN°............[].......

n1 ...........^

LN1 : 0 1 1 1 1

n2................^

LN2 : 0 1 1 1 1

n°................^......

LN°............[].......

n1 ...........^

LN1 : 0 1 1 1 1

n2................^

LN2 : 0 1 1 1 1

n°.............^......

LN°.........[].......

n1 ...........^

LN1 : 0 1 1 1 1

n2.............^

LN2 : 0 1 1 1 1

n°.............^......

LN°.........[].......

n1 ...........^

LN1 : 0 1 1 1 1

IGS(p) Si LN1 n1 +/- Si -> GX€(p)i

IGA.4 IGS(1) 1 LN1 -3 -1 1 -> IGS(1)1


IGA.4 IGS(1)1 1 LN1 -4 0 1 -> IG€(1)1

GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)ij

IGA.4 IG€(1)1 [ ] LN° -3 -1 [ ] -> IG£(1)1[]

GX£(p)ij £k LN2 n2 +/- £k r/w £k LN2 n2 +/- GXS(p)

IGA.4 IG£(1)1[] 1 LN2 -3 -1 1 r/w 1 LN2 -3 -1 IGS(1)

GXS(p) Si LN1 n1 +/- Si -> GXS(p)i

IGA.5 IGS(1) 0 LN1 -4 -1 0 -> IGS(1)0

04/03/2012 C.G[Texte]

n2.............^

LN2 : 0 1 1 1 1

n°.............^......

LN°.........[].......

n1 .........^

LN1 : [] 0 1 1 1 1

n2.............^

LN2 : 0 1 1 1 1

n°.............^......

LN°.........[].......

n1 .........^

LN1 : [] 0 1 1 1 1

n2.............^

LN2 : 0 1 1 1 1

n°...........^......

LN°.......[].......

n1 .........^

LN1 : [] 0 1 1 1 1

n2.......... ^

LN2 : [] 0 1 1 1 1

n°...........^......

LN°.......[].......

n1 .........^

LN1 : [] 0 1 1 1 1

IGA.5 GXS(p)i [-] LX1 n1 0 Si -> GX€(p)i

IGA.5 IGS(1)0 [-] LN1 -5 0 [-] -> IG€(1)0

GX€(p)i [ ] LN° n° +/- [ ] -> GX£(p)i[]

IGA.5 IG€(1)0 [ ] LN° -4 -1 [ ] -> IG£(1)0[]

IG£(p)i[] 0 LN2 n2 +/- 0 r/w 0 LN2 n2 +/- GXS(p)

IGA.5 IG£(1)0[] 0 LN2 -4 -1 0 r/w 0 LN2 n2 -1 IGS(1)

GXS(p) [-] LX1 n1 -0 [-] -> GXS.cc5

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

IGA.6 IGS(1) [-] LN1 -5 -0 [-] IGS.cc5

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

04/03/2012 C.G[Texte]

n2.......... ^

LN2 : [] 0 1 1 1 1

n°........... ^......

LN°.......[].......

n1 ......... ^

LN1 : [] 0 1 1 1 1

Grouping together

IGS.cc2 ! +

IGA.1 IGS(1) 1 LN1 0 -1 1 -> IGS(1)1

IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1

IGA.1 IG€(1)1 [ ] LN° 0 -1 [ ] -> IG£(1)1[]

IGA.1 IG£(1)1[] 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)

IGA.2 IGS(1) 1 LN1 -1 -1 1 -> IGS(1)1

IGA.2 IGS(1)1 1 LN1 -2 0 1 -> IG€(1)1

IGA.2 IG€(1)1 [ ] LN° -1 -1 [ ] -> IG£(1)1[]

IGA.2 IG£(1)1[] 1 LN2 -1 -1 1 -> IGS(1)

IGA.3 IGS(1) 1 LN1 -2 -1 1 -> IGS(1)1

IGA.3 IGS(1)1 1 LN1 -3 0 1 -> IG€(1)1

IGA.3 IG€(1)1 [ ] LN° -2 -1 [ ] -> IG£(1)1[]

IGA.3 IG£(1)1[] 1 LN2 -2 -1 1 r/w 1 LN2 -2 -1 IGS(1)

IGA.4 IGS(1) 1 LN1 -3 -1 1 -> IGS(1)1

IGA.4 IGS(1)1 1 LN1 -4 0 1 -> IG€(1)1

IGA.4 IG€(1)1 [ ] LN° -3 -1 [ ] -> IG£(1)1[]

IGA.4 IG£(1)1[] 1 LN2 -3 -1 1 r/w 1 LN2 -3 -1 IGS(1)

IGA.5 IGS(1) 0 LN1 -4 -1 0 -> IGS(1)0

IGA.5 IGS(1)0 [ ] LN1 -5 0 [ ] -> IG€(1)0

IGA.5 IG€(p)0 [ ] LN° -4 -1 [ ] -> IG£(1)0[]

IGA.5 IG£(1)0[] 0 LN2 -4 -1 0 r/w 0 LN2 -4 -1 IGS(1)

IGA.6 IGS(1) [-] LN1 -5 - 0 [-] -> IGS.cc5

04/03/2012 C.G[Texte]

Identification table

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

IGS.cc2 ! +

IGA.1 IGS(1) 1 LN1 0 -1 1 -> IGS(1)1

IGA.2 IGS(1) 1 LN1 -1 -1 1 -> IGS(1)1

IGA.3 IGS(1) 1 LN1 -2 -1 1 -> IGS(1)1

IGA.4 IGS(1) 1 LN1 -3 -1 1 -> IGS(1)1

IGA.5 IGS(1) 0 LN1 -4 -1 0 -> IGS(1)0

IGA.6 IGS(1) [-] LN1 -5 - 0 [-] -> IGS.cc5

IGA.1 IGS(1)1 1 LN1 -1 0 1 -> IG€(1)1

IGA.2 IGS(1)1 1 LN1 -2 0 1 -> IG€(1)1

IGA.3 IGS(1)1 1 LN1 -3 0 1 -> IG€(1)1

IGA.4 IGS(1)1 1 LN1 -4 0 1 -> IG€(1)1

IGA.5 IGS(1)0 [ ] LN1 -5 0 [ ] -> IG€(1)0

IGA.1 IG€(1)1 [ ] LN° 0 -1 [ ] -> IG£(1)1[]

IGA.2 IG€(1)1 [ ] LN° -1 -1 [ ] -> IG£(1)1[]

IGA.3 IG€(1)1 [ ] LN° -2 -1 [ ] -> IG£(1)1[]

IGA.4 IG€(1)1 [ ] LN° -3 -1 [ ] -> IG£(1)1[]

IGA.5 IG€(p)0 [ ] LN° -4 -1 [ ] -> IG£(1)0[]

IGA.1 IG£(1)1[] 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)

IGA.2 IG£(1)1[] 1 LN2 -1 -1 1 r/w 1 LN2 -1 -1 IGS(1)

IGA.3 IG£(1)1[] 1 LN2 -2 -1 1 r/w 1 LN2 -2 -1 IGS(1)

IGA.4 IG£(1)1[] 1 LN2 -3 -1 1 r/w 1 LN2 -3 -1 IGS(1)

IGA.5 IG£(1)0[] 0 LN2 -4 -1 0 r/w 0 LN2 -4 -1 IGS(1)

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

IGS.cc2 ! +

04/03/2012 C.G[Texte]

Généralisation des positions

IGA.1 IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGA.2 IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGA.3 IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGA.4 IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGA.5 IGS(1) 0 LN1 n1 -1 0 -> IGS(1)0

IGA.6 IGS(1) [-] LN1 n1 - 0 [-] -> IGS.cc5

IGA.1 IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGA.2 IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGA.3 IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGA.4 IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGA.5 IGS(1)0 [ ] LN1 n1 0 [ ] -> IG€(1)0

IGA.1 IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IGA.2 IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IGA.3 IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IGA.4 IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IGA.5 IG€(p)0 [ ] LN° n° -1 [ ] -> IG£(1)0[]

IGA.1 IG£(1)1[] 1 LN2 n2 -1 1 r/w 1 LN2 n2 -1 IGS(1)





IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

IGS.cc2 ! +

04/03/2012 C.G[Texte]

Cross-checking

IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

IGS(1) 0 LN1 n1 -1 0 -> IGS(1)0

IGS(1) [-] LN1 n1 - 0 [-] -> IGS.cc5

IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGS(1)0 [ ] LN1 n1 0 [ ] -> IG€(1)0

IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IG€(1)0 [ ] LN° n° -1 [ ] -> IG£(1)0[]

IG£(1)1[] 1 LN2 n2 -1 1 r/w 1 LN2 n2 -1 IGS(1)

IG£(1)0[] 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 IGS(1)

IGS.cc5 [-] LX1 -5 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° -5 +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 -5 +1 [-] -> IGS.cc2

IGS.cc2 ! +

04/03/2012 C.G[Texte]

Opérator IG

IGS(1) 1 LN1 n1 -1 1 -> IGS(1)1

0 LN1 n1 -1 0 -> IGS(1)0

[-] LN1 n1 0 [-] -> IGS.cc5

IGS(1)1 1 LN1 n1 0 1 -> IG€(1)1

IGS(1)0 [ ] LN1 n1 0 [ ] -> IG€(1)0

IG€(1)1 [ ] LN° n° -1 [ ] -> IG£(1)1[]

IG€(1)0 [ ] LN° n° -1 [ ] -> IG£(1)0[]

IG£(1)1[] 1 LN2 n2 -1 1 r/w 1 LN2 n2 -1 IGS(1)

IG£(1)0[] 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 IGS(1)

IGS.cc5 [-] LX1 n1 +1 [-] -> IG€.cc5

IG€.cc5 [-] LX° n° +1 [-] -> IG£.cc5

IG£.cc5 [-] LX2 n2 +1 [-] -> IGS.cc2

IGS.cc2 ! +

04/03/2012 C.G[Texte]

3.B3 OPERATOR GG

From the position the more right of a group of signs GGI, GG operator resets to zero all signs

placed his left by step GGI.1, GGI.2... up to his meeting with a sign of separation [].

An observer can see the effects of the action of the GG operator on the GGI group

^ ^

[ ] 1 0 1 1-> [ ] 0 0 0 0

Analysis grid




[+] LX1 n1 0 [+] -> GXS.cc4

[-] LX1 n1 0 [-] -> GXS.cc5

[/] LX1 n1 0 [/] -> GXS.cc3

GXS(p)i Si/Si LX1 n1 0 Si -> GX€(p)i



GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)




[ ] LX2 n2 +/- [ ] -> GXS(p)

GX£(p)ik £k LX2 n2 +/- £k w £k LX2 n2 +/- GX£p)ik



[ ] LX2 n2 +/- [ ] -> GXS(p)

04/03/2012 C.G[Texte]

Description of the operator GG

The domain in which this is GG operator includes the signs 1 and 0 and with respect to

spacing [] cuts.

The observed phenomenon may represent thus:

n2................... ^

LN2 : [] 0 0 0 0

n°....................^

LN° []

n1...................^

LN1 : [] 1 0 1 1

LN1 is the initial situation and LN2 the situation after the action of the operator GG.

The index position n1 = 0 on LN1 originally of treatment towards moves by step successive

(GGI.1, GGI.2).... on the characters to the left by putting zero.




[] LX1 n1 0 [] -> GXS.cc2

GXS.cc2 ! +

GXS.cc3 [/] LX1 n1 +1 [/] -> GX€.cc3

GX€.cc3 [ ] LX° n° +1 [ ] -> GX£.cc3

GX£.cc3 [ ] LX2 n2 +1 [ ] -> GXS.cc2

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

04/03/2012 C.G[Texte]

In this first phase, the index "^" on LN1 is moved-1 (moving from right to left) and the

GGS(1) initial state is transferred to GG€ (1) 1

n2................... ^

LN2 : [] 0 0 0 0

n°....................^

LN° []

n1...................^

LN1 : [] 1 0 1 1

In the same step, this movement is reflected in a second phase on the way LN° by a

movement of the index of –1 and a transfer of State GG€ (1) 1 in GG £ (p)

n2........................^

LN4 : 0 1 1 1 1

n° :...................^

LN° :..................[]

n 1....................^

LN1 : 0 1 1 1 1

In the last phase of this stage, the r/w action copies the character 0.

n2........................^

LN4 : 0 1 1 1 1

n° :................^...

LN° :...............[]

n 1.................... ^..

LN1 : 0 1 1 1 1

The device is ready to perform a new step GGI.2 of the analysis of the GGI group through the

GG operator, will thus be up to the spacing of the end and its treatment of cut CGS.cc5

Analyses of these steps are categorized according to the different States GGS, GG€,

GXS(1) Si LX1 n1 +/- Si -> GX€(p)i

GGI.1 GGS(1) 1 LN1 0 -1 1 -> GG€(1)1


GX€(p)1 [ ] LN° n° +/- [ ] -> GX£(p)1[


GX£(p)ij £k LN2 n2 +/- £k r/w £k LN2 n2 +/- GXS(p)

GGI.1 GG£(1)1[ 1 LN2 0 -1 1 r/w 1 LN2 0 -1 IGS(1)

GGI.5 GGS(1) [-] LN1 - 4 - 0 [-] -> GGS.cc5

GGS.cc5 [-] LN1 -4 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° -4 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 -4 +1 [ ] -> GXS.cc2

04/03/2012 C.G[Texte]

GG £ ..…… .and are identification tables.

The approximation of the tables with the General model of grid given above allow to override

its N relative positions to the absolute values of the tables.

On generalized tables, is to put duplication to highlight in this way. The reorganization of the

elements remaining after these overlap gives the desired operator.

OPERATOR GG

D : { 1, 0 } { [] }

Statement of changes

n2................... ^

LN2 : [] 0 0 0 0

n°....................^

LN° []

n1...................^

LN1 : [] 1 0 1 1

n2...................^

LN2 : [] 0 0 0 0

n°....................^

LN° []

n1................^

LN1 : [] 1 0 1 1

n2...................^

LN2 : [] 0 0 0 0

n°....................^

LN° []

n1................^

LN1 : [] 1 0 1 1



SI LX1 n1 +/- SI -> GXS(p)i

[+] LX1 n1 0 [+] -> GXS.cc4

[-] LX1 n1 0 [-] -> GXS.cc5

[/] LX1 n1 0 [/] -> GXS.cc3


GGI.1 GGS(1) 1 LN1 0 -1 1 -> GGS(1)1


GGI.1 GGS(1)1 1 LN1 -1 0 1 -> GG€1)1[

04/03/2012 C.G[Texte]

n2...................^

LN2 : [] 0 0 0 0

n°.................^

LN° []

n1................^

LN1 : [] 1 0 1 1

n2................^

LN2 : [] 0 0 0 0

n°.................^

LN° []

n1................^

LN1 : [] 1 0 1 1

n2................^

LN2 : [] 0 0 0 0

n°.................^

LN° []

n1.............^

LN1 : [] 1 0 1 1

n2................^

LN2 : [] 0 0 0 0

n°.................^

LN° []

n1.............^

LN1 : [] 1 0 1 1

n2................^

LN2 : [] 0 0 0 0

n°..............^

LN° []

n1.............^

LN1 : [] 1 0 1 1

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

GG€(1)1 [ ] LX° 0 -1 [ ] -> GG£1)1[


GGI.1 GG£1)1[ 0 LN2 0 -1 0 r/w 0 LN2 0 -1 GGS(1)

GXS(1) Si LX1 n1 +/- Si -> GXS(p)i

GGI.2 GGS(1) 1 LN1 -1 -1 1 -> GGS1)1[


GXS(1)1 0 LN1 -2 0 0 -> GG€(1)1

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)ij

GGI.2 GG€(1)1 [ ] LN° -1 -1 [ ] -> GG£1)1[


GGI.2 GG£1)1[ 0 LN2 -1 -1 0 r/w 0 LN2 -1 -1 GGS(1)

04/03/2012 C.G[Texte]

n2.............^

LN2 : [] 0 0 0 0

n°.............^

LN° []

n1.............^

LN1 : [] 1 0 1 1

n2.............^

LN2 : [] 0 0 0 0

n°.............^

LN° []

n1..........^

LN1 : [] 1 0 1 1

n2.............^

LN2 : [] 0 0 0 0

n°.............^

LN° []

n1..........^

LN1 : [] 1 0 1 1

n2.............^

LN2 : [] 0 0 0 0

n°...........^

LN° []

n1..........^

LN1 : [] 1 0 1 1

n2..........^

LN2 : [] 0 0 0 0

n°...........^

LN° []

n1..........^

LN1 : [] 1 0 1 1

GXS(1) Si LX1 n1 +/- Si -> GXS(p)i

GGI.3 GGS(1) 0 LN1 -2 -1 0 -> GGS(1)0


GXS(1)0 1 LX1 -3 0 1 -> GX€(1)0

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)ij

GGI.3 GG€1)0 [ ] LN° -2 -1 [ ] -> GG£1)0[


GGI.3 GG£1)0[ 0 LN2 -2 -1 0 r/w 0 LN2 -2 -1 GGS(1)


04/03/2012 C.G[Texte]

n2..........^

LN2 : [] 0 0 0 0

n°...........^

LN° []

n1.......^

LN1 : [] 1 0 1 1

n2..........^

LN2 : [] 0 0 0 0

n°...........^

LN° []

n1.......^

LN1 : [] 1 0 1 1

n2..........^

LN2 : [] 0 0 0 0

n°........^

LN° []

n1.......^

LN1 : [] 1 0 1 1

n2.......^

LN2 : [] 0 0 0 0

n°........^

LN° []

n1.......^

LN1 : [] 1 0 1 1

GGI.4 GGS(1) 1 LN1 -3 -1 1 -> GGS1)1


GGS(1)1 [-] LX1 -4 0 [-] -> GG€(1)1

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)ij

GGI.4 GG€1)1 [ ] LN° -3 -1 [ ] -> GG£1)1[


GGI.4 GG£1)1[ 0 LN2 -3 -1 0 r/w 0 LN2 -3 -1 GGS(1)

GXS(p) [-] LX1 n1 +/- [-] -> GXA.cc5

GGI.5 GGS(1) [-] LN1 - 4 0 [-] -> GGS.cc5

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [ ] LX° n° +1 [ ] -> GX£.cc5

GX£.cc5 [ ] LX2 n2 +1 [ ] -> GXS.cc2

GGS.cc5 [-] LN1 -4 +1 [-] -> GG€.cc5

04/03/2012 C.G[Texte]

n2..........^

LN2 : [] 0 0 0 0

n°...........^

LN° []

n1..........^

LN1 : [] 1 0 1 1

GG€.cc5 [ ] LN° -4 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 -4 +1 [ ] -> GXS.cc2

GGS.cc2 ! +

04/03/2012 C.G[Texte]

Grouping together

GGI.1 GGS(1) 1 LN1 0 -1 1 -> GGS(1)1

GGI.1 GGS(1)1 1 LN1 -1 0 1 -> GG€1)1[

GGI.1 GG€(1)1 [ ] LN° 0 -1 [ ] -> GG£1)1[

GGI.1 GG£1)1[ 0 LN2 0 -1 0 r/w 0 LN2 0 -1 GGS(1)

GGI.2 GGS(1) 1 LN1 -1 -1 1 -> GGS1)1[

GGI.2 GXS(1)1 0 LN1 -2 0 0 -> GG€(1)1

GGI.2 GG€(1)1 [ ] LN° -1 -1 [ ] -> GG£1)1[

GGI.2 GG£1)1[ 0 LN2 -1 -1 0 r/w 0 LN2 -1 -1 GGS(1)

GGI.3 GGS(1) 0 LN1 -2 +/- 0 -> GGS(1)0

GGI.3 GXS(1)0 1 LN1 -3 0 1 -> GX€(1)0

GGI.3 GG€1)0 [ ] LN° -2 -1 [ ] -> GG£1)0[

GGI.3 GG£1)0[ 0 LN2 -2 -1 0 r/w 0 LN2 -2 -1 GGS(1)

GGI.4 GGS(1) 1 LN1 -3 -1 1 -> GGS1)1

GGI.4 GGS(1)1 [-] LN1 -4 0 [-] -> GG€(1)1

GGI.4 GG€1)1 [ ] LN° -3 -1 [ ] -> GG£1)1[

GGI.4 GG£1)1[ 0 LN2 -3 -1 0 r/w 0 LN2 -3 -1 GGS(1)

GGI.5 GGS(1) [-] LN1 - 4 - 0 [-] -> GGS.cc5

GGS.cc5 [-] LN1 -4 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° -4 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 -4 +1 [ ] -> GXS.cc2

04/03/2012 C.G[Texte]


GGS.cc2 ! +

GGI.1 GGS(1) 1 LN1 0 -1 1 -> GGS(1)1

GGI.2 GGS(1) 1 LN1 -1 -1 1 -> GGS1)1

GGI.3 GGS(1) 0 LN1 -2 +/- 0 -> GGS(1)0

GGI.4 GGS(1) 1 LN1 -3 -1 1 -> GGS1)1

GGI.5 GGS(1) [-] LN1 - 4 - 0 [-] -> GGS.cc5

GGI.1 GGS(1)1 1 LN1 -1 0 1 -> GG€1)1[

GGI.2 GXS(1)1 0 LN1 -2 0 0 -> GG€(1)1

GGI.3 GXS(1)0 1 LN1 -3 0 1 -> GX€(1)0

GGI.4 GGS(1)1 [-] LN1 -4 0 [-] -> GG€(1)1

GGI.1 GG€(1)1 [ ] LX° 0 -1 [ ] -> GG£1)1[

GGI.2 GG€(1)1 [ ] LN° -1 -1 [ ] -> GG£1)1[

GGI.3 GG€1)0 [ ] LN° -2 -1 [ ] -> GG£1)0[

GGI.4 GG€1)1 [ ] LN° -3 -1 [ ] -> GG£1)1[

GGI.1 GG£1)1[ 0 LN2 0 -1 0 r/w 0 LN2 0 -1 GGS(1)

GGI.2 GG£1)1[ 0 LN2 -1 -1 0 r/w 0 LN2 -1 -1 GGS(1)

GGI.3 GG£1)0[ 0 LN2 -2 -1 0 r/w 0 LN2 -2 -1 GGS(1)

GGI.4 GG£1)1[ 0 LN2 -3 -1 0 r/w 0 LN2 -3 -1 GGS(1)

GGS.cc5 [-] LN1 -4 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° -4 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 -4 +1 [ ] -> GXS.cc2

04/03/2012 C.G[Texte]


GGS.cc2 ! +

GGI.1 GGS(1) 1 LN1 n1 -1 1 -> GGS(1)1

GGI.2 GGS(1) 1 LN1 n1 -1 1 -> GGS1)1

GGI.3 GGS(1) 0 LN1 n1 -1 0 -> GGS(1)0

GGI.4 GGS(1) 1 LN1 n1 -1 1 -> GGS1)1

GGI.5 GGS(1) [-] LN1 n1 - 0 [-] -> GGS.cc5

GGI.1 GGS(1)1 1 LN1 n1 0 1 -> GG€(1)1

GGI.2 GXS(1)1 0 LN1 n1 0 0 -> GG€(1)1

GGI.3 GXS(1)0 1 LN1 n1 0 1 -> GX€(1)0

GGI.4 GGS(1)1 [-] LN1 n1 0 [-] -> GG€(1)1

GGI.1 GG€(1)1 [ ] LN° n° -1 [ ] -> GG£1)1[

GGI.2 GG€(1)1 [ ] LN° n° -1 [ ] -> GG£1)1[

GGI.3 GG€(1)0 [ ] LN° n° -1 [ ] -> GG£1)0[

GGI.4 GG€(1)1 [ ] LN° n° -1 [ ] -> GG£1)1[

GGI.1 GG£1)1[ 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 GGS(1)




GGS.cc5 [-] LN1 -4 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° -4 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 -4 +1 [ ] -> GXS.cc2

04/03/2012 C.G[Texte]

Cross-checking

Opérator GG

GGS.cc2 ! +

GGI.1 GGS(1) 1 LN1 n1 -1 1 -> GGS(1)1

GGI.3 GGS(1) 0 LN1 n1 -1 0 -> GGS(1)0

GGI.5 GGS(1) [-] LN1 n1 0 [-] -> GGS.cc5

GGI.1 GGS(1)1 1 LN1 n1 0 1 -> GG€(1)1

GGI.2 GXS(1)1 0 LN1 n1 0 0 -> GG€(1)1

GGI.3 GGS(1)0 1 LX1 n1 0 1 -> GG€(1)0

GGI.4 GGS(1)1 [-] LX1 n1 0 [-] -> GG€(1)1

GGI.1 GG€(1)1 [ ] LX° n° -1 [ ] -> GG£1)1[

GGI.3 GG€(1)0 [ ] LN° n° -1 [ ] -> GG£1)0[



GGS.cc5 [-] LN1 n1 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° n1 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 n1 +1 [ ] -> GXS.cc2

GGS.cc2 ! +

04/03/2012 C.G[Texte]

3.B4 GROUP SUBSTITUTION

The operator DE overrides a new group of variable to a former group also length of variable-

length character.

ABCDE ->ACBHDE

The groups are designated by the bold which constitute.

This style of substitution is often used in mathematical reasoning.

Analysis grid

GGS(1) 1 LN1 n1 -1 1 -> GGS(1)1

0 LN1 n1 -1 0 -> GGS(1)0

[-] LN1 n1 0 [-] -> GGS.cc5

GGS(1)1 1 LN1 n1 0 1 -> GG€(1)1

0 LN1 n1 0 0 -> GG€(1)1

[-] LX1 n1 0 [-] -> GG€(1)1

GGS(1)0 1 LX1 n1 0 1 -> GG€(1)0

GG€(1)1 [ ] LN° n° -1 [ ] -> GG£1)1[

GG€1)0 [ ] LN° n° -1 [ ] -> GG£1)0[

GG£1)1[ 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 GGS(1)

GG£1)0[ 0 LN2 n2 -1 0 r/w 0 LN2 n2 -1 GGS(1)

GGS.cc5 [-] LN1 n1 +1 [-] -> GG€.cc5

GG€.cc5 [ ] LN° n1 +1 [ ] -> GG£.cc5

GX£.cc5 [ ] LN2 n1 +1 [ ] -> GXS.cc2

GGS.cc2 ! +




[+] LX1 n1 0 [+] -> GXS.cc4

[-] LX1 n1 0 [-] -> GXS.cc5

[/] LX1 n1 0 [/] GXS.cc3

04/03/2012 C.G[Texte]




GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)




[ ] LX2 n2 +/- [ ] -> GXS(p)


£r LX2 n2 +/- £r r/w £r LX2 n2 +/- GXS(p)


[ ] LX2 n2 +/- [ ] -> GXS(p)



[] LX1 n1 0 [] -> GXS.cc2

GXS.cc2 ! +

GXS.cc3 [/] GX1 n1 +1 [/] -> GX€.cc3

GX€.cc3 [ ] GX° n° +1 [ ] -> GX£.cc3

04/03/2012 C.G[Texte]

Description of the functioning the operator DE

From a text which reflects a given substitution BC-> BC

ABCDE ->ACBDE

The analysis grid allow to develop a procedure to achieve this result.

The representative observed change image, original ABCDE is on line 1 while the final text is

on the line of2.

DE° Line contains only a spacing no intermediate event being observed.

n2 : ^

DE2 : A C B DE

n° : ^

DE° : []

n : ^

DE1 : A B C D E

The grid saves no change in position1 and initial state on 1 DE(1) transforms into A DE(1).

n2 : ^

DE2 : A C B DE

n° : ^

DE° : []

n : ^

DE1 : A B C D E

GX£.cc3 [ ] GX2 n2 +1 [ ] -> GXS.cc2

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2



D01.1 DES(1) A DE1 1 +1 A -> DES(1)A

04/03/2012 C.G[Texte]

DE€ (1)A after registration of the character following B transforms in turn in of DE£ (1) A []

the final State on DE2

n2 : ^

DE2 : A C B DE

n° : ^

DE° : []

n1 : ^

DE1 : A B C D E

In cases where the character (l) read is reported in bold, the analysis path will be different as

shown in the grid

and in this case GXS (p) i turns into GX€ (p) i and then GXS (p), GXS (p) i agree with the

bold of the sign following "C".

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n 1 : ^

DE1 : A B C D E

When the analysis of the original text again encounters a character without overload of fatty,

the path of the transfers this analysis on the first bold line DE2 unchanged position and they

will substitute for the old in the use of the operator DE.

The end of the bold signals return to a simple transformation by character.

A new application of {BC-> CB} terrmine this description


DES(1)A B DE1 2 0 B -> DE€(1)A


GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

D01.1 DE€(1)A [ ] DE° 1 +1 [ ] DE£1)A[]




GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)

D01.3 DE€(1)B [ ] DE° 2 +1 [ ] -> DES(1)


DES(1) C DE1 3 +1 C -> DES(1)C

04/03/2012 C.G[Texte]

OPERATEUR : DE (BC->CB)

D : {A, B ,C, D, E} {[ ]}

TXT : ABCDE ->ACBDE

Statement of changes

n2 : ^

DE2 : A C B DE

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B DE

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B DE



D01.1 DES(1) A DE1 1 +1 A -> DES(1)A


DES(1)A B DE1 2 0 B -> DE€(1)A

04/03/2012 C.G[Texte]

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^ DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E


GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

D01.1 DE€(1)A [ ] DE° 1 +1 [ ] DE£1)A[]


G.E DE£1)A[] A DE2 1 +1 A r/w A DE2 1 +1 DES(1)


D01.2 DES(1) B DE1 2 +1 B -> DES(1)B


D01.2 DES(1)B C DE1 3 0 C -> DE€(1)B

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)

D01.3 DE€(1)B [ ] DE° 2 +1 [ ] -> DES(1)

04/03/2012 C.G[Texte]

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E


DES(1) C DE1 3 +1 C -> DES(1)C

GXS(p)i Si/Si LX1 n1 +/- Si/Si -> GX€(p)i

D01.3 DES(1)C D DE1 4 0 D -> DE€(1)C

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)

D01.3 DE€(1)C [ ] DE° 3 +1 [ ] DES(1)


DES(1) D DE1 4 +1 D -> DES(1)D


DES(1)D E DE1 5 0 E -> DE€(1)D

04/03/2012 C.G[Texte]

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

n2 : ^

DE2 : A C B D E

n° : ^

DE° : []

n : ^

DE1 : A B C D E

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

DE€(1)D [ ] DE° 4 +1 [ ] -> DE£1)D[

GX£(p)i[] £k LX2 n2 +/- £k r/w £k LX2 n2 +/- GX£(p)ik

D01.3 DE£1)D[ C DE2 2 +1 C r/w C DE2 2 +/- DE£1DC

GX£(p)i[] £k LX2 n2 +/- £k r/w £k LX2 n2 +/- GX£(p)ik

D01.3 DE£1DC B DE2 3 +1 B r/w B DE2 3 +/- DE£1DB

GX£p)iB £k LX2 n2 +/- £k r/w £k LX2 n2 +/- GXS(p)

DE£1DB D DE2 4 +1 D r/w D DE2 4 +1 DES(1)


DES(1) E DE1 5 +1 E -> DES(1)E

04/03/2012 C.G[Texte]

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []


DES(1)E [ ] DE1 6 0 [ ] -> DE€(1)E

GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

DE€(1)E [ ] DE° 5 +1 [ ] -> DE£1)E[


DE£1)E[] E DE2 5 +1 £k r/w E DE2 5 +1 DES(1)

GXS(p) [+] LX1 n1 -1 [+] -> GXS.cc4

DES(1) [+] DE1 6 0 [+] -> DES.cc4

GXS.cc4 [+] LX1 n1 0 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

04/03/2012 C.G[Texte]

n2 : ^

DE2 : A C B D E []

n° : ^

DE° : []

n : ^

DE1 : A C B D E []

Grouping together

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

DES.cc4 [+] DE1 n1 0 [+] -> DE€.cc4

DE€.cc4 [+] DE° n° -1 [+] -> DE£.cc4

DE£.cc4 [+] DE2 n2 -1 [+] -> DES.cc2

D01.1 DES(1) A DE1 1 +1 A -> DES(1)A

D01.1 DES(1)A B DE1 2 0 B -> DE€(1)A

D01.1 DE€(1)A [ ] DE° 1 +1 [ ] DE£1)A[]

D01.1 DE£1)A[] A DE2 1 +1 A r/w A DE2 1 +1 DES(1)

D01.2 DES(1) B DE1 2 +1 B -> DES(1)B

D01.2 DES(1)B C DE1 3 0 C -> DE€(1)B

D01.2 DE€(1)B [ ] DE° 2 +1 [ ] -> DES(1)

D01.3 DES(1) C DE1 3 +1 C -> DES(1)C

D01.3 DES(1)C D DE1 4 0 D -> DE€(1)C

D01.3 DE€(1)C [ ] DE° 3 +1 [ ] DES(1)

D01.4 DES(1) D DE1 4 +1 D -> DES(1)D

D01.4 DES(1)D E DE1 5 0 E -> DE€(1)D

D01.4 DE€(1)D [ ] DE° 4 +1 [ ] -> DE£1)D[

D01.3 DE£1)D[ C DE2 2 +1 C r/w C DE2 2 +1 DE£1DC

D01.3 DE£1DC B DE2 3 +1 B r/w B DE2 3 +1 DE£1DB

04/03/2012 C.G[Texte]


D01.4 DE£1DB D DE2 4 +1 D r/w D DE2 4 +1 DES(1)

D01.5 DES(1) E DE1 5 +1 E -> DES(1)E

D01.5 DES(1)E [ ] DE1 6 0 [ ] -> DE€(1)E

D01.5 DE€(1)E [ ] DE° 5 +1 [ ] -> DE£1)E[

D01.5 DE£1)E[] E DE2 5 +1 £k r/w E DE2 5 +1 DES(1)

D01.6 DES(1) [+] DE1 6 -1 [+] -> DES.cc4

D01.1 DES(1) A DE1 1 +1 A -> DES(1)A

D01.2 DES(1) B DE1 2 +1 B -> DES(1)B

D01.3 DES(1) C DE1 3 +1 C -> DES(1)C

D01.4 DES(1) D DE1 4 +1 D -> DES(1)D

D01.5 DES(1) E DE1 5 +1 E -> DES(1)E

D01.6 DES(1) [+] DE1 6 -1 [+] -> DES.cc4

D01.1 DES(1)A B DE1 2 0 B -> DE€(1)A

D01.2 DES(1)B C DE1 3 0 C -> DE€(1)B

D01.3 DES(1)C D DE1 4 0 D -> DE€(1)C

D01.4 DES(1)D E DE1 5 0 E -> DE€(1)D

D01.5 DES(1)E [ ] DE1 6 0 [ ] -> DE€(1)E

D01.1 DE€(1)A [ ] DE° 1 +1 [ ] DE£1)A[]

D01.2 DE€(1)B [ ] DE° 2 +1 [ ] -> DES(1)

D01.3 DE€(1)C [ ] DE° 3 +1 [ ] DES(1)

D01.4 DE€(1)D [ ] DE° 4 +1 [ ] -> DE£1)D[

04/03/2012 C.G[Texte]


D01.5 DE€(1)E [ ] DE° 5 +1 [ ] -> DE£1)E[

D01.1 DE£1)A[] A DE2 1 +1 A r/w A DE2 1 +1 DES(1)

D01.3 DE£1)D[ C DE2 2 +1 C r/w C DE2 2 +1 DE£1DC

D01.3 DE£1DC B DE2 3 +1 B r/w B DE2 3 +1 DE£1DB

D01.4 DE£1DB D DE2 4 +1 D r/w D DE2 4 +1 DES(1)

D01.5 DE£1)E[] E DE2 5 +1 £k r/w E DE2 5 +1 DES(1)

D01.1 DES(1) Si DE1 n1 +1 Si -> DES(1)i

D01.2 DES(1) B DE1 n1 +1 B -> DES(1)B

D01.3 DES(1) C DE1 n1 +1 C -> DES(1)C

D01.4 DES(1) Si DE1 n1 +1 Si -> DES1)Si

D01.5 DES(1) Si DE1 n1 +1 Si -> DES1)Si

D01.6 DES(1) [+] DE1 n1 -1 [+] -> DES.cc4

D01.1 DES1)Si B DE1 n1 0 B -> DE€(1)Si

D01.2 DES(1)B C DE1 n1 0 C -> DE€(1)B

D01.3 DES(1)C Si DE1 n1 0 Si -> DE€(1)C

D01.4 DES1)Si Si DE1 n1 0 Si -> DE€(1)Si

D01.5 DES1)Si [ ] DE1 n2 0 [ ] -> DE€1)Si

D01.1 DE€(1)Si [ ] DE° n° +1 [ ] DE£1)i[]

D01.2 DE€(1)B [ ] DE° n° +1 [ ] -> DES(1)

D01.3 DE€(1)C [ ] DE° n° +1 [ ] DES(1)

04/03/2012 C.G[Texte]

Cross-checking

D01.4 DE€(1)Si [ ] DE° n° +1 [ ] -> DE£1)i[]

D01.5 DE€(1)Si [ ] DE° n° +1 [ ] -> DE£1)i[]

D01.1 DE£1)i[] £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DES(1)

D01.3 DE£1)i[] C DE2 n2 +1 C r/w £k DE2 n2 +1 DE£1)iC

D01.3 DE£1)iC B DE2 n2 +1 B r/w B DE2 n2 +1 DE£1)iB

D01.4 DE£(1)iB £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DES(1)


D01.1 DES(1) Si DE1 n1 +1 Si -> DES(1)Si

D01.2 DES(1) B DE1 n1 +1 B -> DES(1)B

D01.3 DES(1) C DE1 n1 +1 C -> DES(1)C

D01.6 DES(1) [+] DE1 n1 -1 [+] -> DES.cc4

D01.2 DES(1)B C DE1 n1 0 C -> DE€(1)B

D01.3 DES(1)C Si DE1 n1 0 Si -> DE€(1)C

D01.4 DES1)Si Si DE1 n1 0 Si -> DE€(1)Si

D01.5 DES1)Si [ ] DE1 n1 0 [ ] -> DE€1)Si

D01.1 DE€(1)Si [ ] DE° n° +1 [ ] DE£1)i[]

D01.2 DE€(1)B [ ] DE° n° +1 [ ] -> DES(1)

D01.3 DE€(1)C [ ] DE° n° +1 [ ] DES(1)


D01.3 DE£1)i[] C DE2 n2 +1 C r/w C DE2 n2 +1 DE£1)iC

D01.3 DE£1)iC B DE2 n2 +1 B r/w B DE2 n2 +1 DE£1)iB

04/03/2012 C.G[Texte]

Opérateur DE {BC->CB}

D01.3 DE£1)iB £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DES(1)

DES(1) Si DE1 n1 +1 Si -> DES1)Si

B DE1 n1 +1 B -> DES(1)B

C DE1 n1 +1 C -> DES(1)C

[+] DE1 n1 -1 [+] -> DES.cc4

DES(1)B C DE1 n1 0 C -> DE€(1)B

DES(1)C Si DE1 n1 0 Si -> DE€(1)C

DES1)Si Si DE1 n1 0 Si -> DE€(1)Si

[ ] DE1 n2 0 [ ] -> DE€1)Si

DE€(1)Si [ ] DE° n° +1 [ ] DE£1)i[]

DE€(1)B [ ] DE° n° +1 [ ] -> DES(1)

DE€(1)C [ ] DE° n° +1 [ ] DES(1)

DE£1)i[] £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DES(1)

DE£1)i[] C DE2 n2 +1 C r/w C DE2 n2 +1 DE£1)iC

DE£1)iC B DE2 n2 +1 B r/w B DE2 n2 +1 DE£1)iB

DE£1)iB £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DES(1)

04/03/2012 C.G[Texte]

Application of the operator DE {BC - CB} to text DO2

D02 : E B C D

DE : {BC-CB}

DE2 :

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 :

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 :

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 :

n° : ^

DE° : []

n : ^ DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

DES(1) Si DE1 n1 +1 a -> DES(1)Si

D02.1 DES(1) E DE1 1 +1 E -> DES(1)E

DES1)Si Si DE1 n1 0 Si -> DE€(1)Si

DES1)E B DE1 2 0 B -> DE€(1)E

D01.1 DE€(1)Si [ ] DE° n° +1 [ ] DE£1)i[]

D01.1 DE€(1)E [ ] DE° 2 +1 [ ] DE£1)E[]


D02.1 DE£1)E[] w E DE2 1 +1 DES(1)

04/03/2012 C.G[Texte]

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

D01.2 DES(1) B DE1 n1 +1 B -> DES(1)B

D02.2 DES(1) B DE1 2 +1 B -> DES(1)B

D01.2 DES(1)B C DE1 n1 0 C -> DE€(1)B

D01.2 DES(1)B C DE1 3 0 C -> DE€(1)B

DE€(1)B [ ] DE° n° +1 [ ] -> DES(1)

DE€(1)B [ ] DE° 2 +1 [ ] -> DES(1)

DES(1) C DE1 n1 +1 C -> DES(1)C

D02.3 DES(1) C DE1 3 +1 C -> DES(1)C

DES(1)C Si DE1 n1 0 Si -> DE€(1)C

DES(1)C D DE1 4 0 D -> DE€(1)C

04/03/2012 C.G[Texte]

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E C

n° : ^

DE° : []

n : ^

DE1 : E B C D []

DE€(1)C [ ] DE° n° +1 [ ] DES(1)

DE€(1)C [ ] DE° 3 +1 [ ] DES(1)

DES(1) Si DE1 n1 +1 Si -> DES1)Si

DES(1) D DE1 4 +1 D -> DES1)D

DES1)Si [ ] DE1 n2 0 [ ] -> DE€1)Si

DES1)D [ ] DE1 5 0 [ ] -> DE€1)D

DE€(1)Si [ ] DE° n° +1 [ ] DE£1)i[]

DE€(1)D [ ] DE° 4 +1 [ ] DE£1)D[

DE£1)i[] £k DE2 n2 +1 £k r/w £k DE2 n2 +1 DE£1iC

DE£1)D[ w C DE2 2 +1 DE£1DC

04/03/2012 C.G[Texte]

n2 : ^

DE2 : E C B

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E C B D []

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E C B D []

n° : ^

DE° : []

n : ^

DE1 : E B C D []

n2 : ^

DE2 : E C B D []

n° : ^

DE° : []

n : ^

DE1 : E B C D []

3.B5 BINARY DIGITAL ADDITION

DE£1)iC B DE2 n2 +1 B w B DE2 n2 +1 DE£1)iB

DE£1DC w B DE2 3 +1 DE£1DB

DE£1)iB £k DE2 n2 +1 £k w £k DE2 n2 +1 DES(1)

DE£1DB w D DE2 4 +1 DES(1)

DES(1) [+] DE1 n1 -1 [+] -> DES.cc4

DES(1) [+] DE1 5 -1 [+] -> DES.cc4

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

DES.cc4 [+] DE1 n1 -1 [+] -> DE€.cc4

DE€.cc4 [+] DE° n° -1 [+] -> DE£.cc4

DE£.cc4 [+] DE2 n2 -1 [+] -> DES.cc2

04/03/2012 C.G[Texte]

It is by apprentice-ship how this device learns to do this type of operation in which the

collected data are gathered successively in the AN operator.

From an image representing the two arguments and the result to obtain, are analyzed using a

grid and an independent process observable changes from an external point of view.

At the end of this work,we get an operator to run binary digital additions following this

process and a table of identification that will allow to recognize later this operator in the

execution of a transaction.

Analysis grid

Changes at each stage of the operation of addition of two binary numerical values are

recorded using the following grid :

Description of binary digital addition

Either bb1101 + bb1011-> b11000, the arguments and the result of a binary addition

These data are transferred on the following image



[+] LX1 n1 0 [+] -> GXS.cc4



GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij



[ ] LX2 n2 +/- [ ] -> GXS(p)


[ ] LX2 n2 +/- [ ] -> GXS(p)


GXS.cc5 [-] LN1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LN° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LN2 n2 +1 [-] -> GXS.cc2

GXS.cc2 ! +

04/03/2012 C.G[Texte]

n1 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1

The index refer to the elements examined

LN1, LN °, LN2 lines that support the arguments and the resulting value of this transaction.

[LN1, N], [LN °, N], [LN2, N] are the positions of these data and [E] their corresponding

values.

The first stage data are thus repeated on the grid:

Can observe the different phases of this first step as indicated in the grid on this image.

The first line in the ANS (1) initial state is set to the value 1 in position 0 and the State

transferred in ANS (1)1.In this State, the following value read in n - 1 is here 0, position -1

and the State becomes AN€ (1) 1 without new increment - 1 of n1.

LN° line is then informed of the value 1 in position 0 that is incremented -1 and the State is

transferred in AN £ (1)11.In the fourth phase, LN2 data are repeated as the elements resulting

from this first step [0, 0].

The State is transferred to the initial state of the next line (1) year for the second stage

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1

G.E Q STQ IMG N D E A E’ IMG N D DC Q'

AN.1 ANS(1) 1 LN1 0 -1 1 -> ANS(1)1

ANS(1)1 0 LN1 -1 0 0 -> AN€(1)1

AN€(1)1 1 LN° 0 -1 1 -> AN£1)11

AN£1)11 0 LN2 0 -1 0 w 0 LN2 0 -1 ANS(1)


AN.2 ANS(1) 0 LN1 -1 -1 0 -> ANS(1)0

ANS(1)0 1 LN1 -2 0 0 -> AN€(1)0

AN€(1)0 1 LN° -1 -1 1 -> AN£1)01

04/03/2012 C.G[Texte]

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1

In this fourth step, change affecting the value 1 on LN2 under State AN£ (1) 11 is no more

similar to the transformations observed in the AN.1 steps

It must be assumed that this first stage caused a mutation in the AN States at the end of this

last phase of step 1 and the new State is maintained until step 4 justifying this new

transformation.

In this hypothesis, the course of the analysis must be resumed from the next step AN2.

AN£1)01 0 LN2 -1 -1 0 w 0 LN2 -1 -1 ANS(1)


AN.3 ANS(1) 1 LN1 -2 -1 1 -> ANS(1)1

ANS(1)1 1 LN1 -3 0 1 -> AN€(1)1

AN€(1)1 0 LN° -2 -1 0 -> AN£1)10

AN£1)10 0 LN2 -2 -1 0 w 0 LN2 -2 -1 ANS(1)


AN.4 ANS(1) 1 LN1 -3 -1 1 -> AN(1)1

ANS(1)1 b LN1 -4 0 Si -> AN€(1)1

AN€(1)1 1 LN° -3 -1 1 -> AN£1)11

AN£1)11 1 LN2 -3 -1 1 x 1 LN2 -3 -1 ANS(1)

f/b 1 LN1 0 -1 ANS(1)

AN.4 AN£1)11 1 LN2 -3 -1 1 x 1 LN2 -3 -1 ANS(1)

AN.1 AN£1)11 0 LN2 0 -1 0 w 0 LN2 0 -1 ANS(1)

04/03/2012 C.G[Texte]

This is achieved by the internal x and fb functions available on the analysis grid. They block

the progress of the analysis because the observed contradiction and cause the return to the first

stage where the change has the occur.

The analysis runs back again with States receiving a new index p=2

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n : ^

LN1 : b b 1 1 0 1

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1


AN.1 ANS(1) 1 LN1 0 -1 1 -> ANS(1)1

ANS(1)1 0 LN1 -1 0 0 -> AN€(1)1

AN€(1)1 1 LN° 0 -1 1 -> AN£1)11

AN£1)11 0 LN2 0 -1 0 -> 0 LN2 0 -1 ANS(2)


AN.2 ANS(2) 0 LN1 -1 -1 0 -> ANS(2)0

ANS(2)0 1 LN1 -2 0 1 AN€(2)0

AN€(2)0 1 LN° -1 -1 1 -> AN£2)01

AN£2)01 0 LN2 -1 -1 0 w 0 LN2 -1 -1 ANS(2)


AN.3 ANS(2) 1 LN1 -2 -1 1 -> ANS(2)1

ANS(2)1 1 LN1 -3 0 1 AN€(2)1

AN€(2)1 0 LN° -2 -1 0 -> AN£2)10

AN£2)10 0 LN° -2 -1 0 w 0 LN2 -2 - ANS(2)

04/03/2012 C.G[Texte]

n2 : ^

LN2 : b 1 1 0 0 0

n° : ^

LN° : b b 1 0 1 1

n1 : ^

LN1 : b b 1 1 0 1


The analysis which was interrupted at this level during the first reading, may be continued

here without contradiction with the coherence between the AN States.

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

The line LN2 step 6 is in contradiction with LN2 step 5


AN.4 ANS(2) 1 LN1 -3 -1 1 -> ANS(2)1

ANS(2)1 b LN1 -4 0 b AN€(2)1

AN€(2)1 1 LN° -3 -1 1 -> AN£2)11

AN£2)11 1 LN2 -3 -1 1 w 1 LN2 -3 - ANS(2)


AN.5 ANS(2) b LN1 -4 -1 b -> ANS(2)b

ANS(2)b b LN1 -5 0 b -> AN€(2)b

AN€(2)b b LN° -4 -1 b -> AN£2)bb

AN£2)bb 1 LN2 -4 -1 1 w 1 LN2 -4 - ANS(2)


AN.6 ANS(2) B LN1 -5 -1 b -> ANS(2)b

ANS(2)b [] LN1 -6 0 [] AN€(2)b

AN€(2)b B LN° -5 -1 b AN£2)bb

AN£2)bb B LN2 -5 -1 b x 0 LN2 -5 -1 ANS(2)

f/b B LN1 -4 -1 ANS(2)

AN.5 AN£2)bb 1 LN2 -4 -1 1 w 1 LN2 -4 - ANS(2)

04/03/2012 C.G[Texte]

It is necessary to assign another index State AN£ (2) bb to escape this contradiction.To avoid

unnecessary inflation, index (1) is again used subject not later meet a new contradiction in this

index.

Analysis resumed at the level of step 5 at the end of phase 4 of this step with index p = 1


n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

AN£2)bb B LN2 -5 -1 b x 0 LN2 -5 -1 ANS(2)


AN.5 ANS(2) b LN1 -4 -1 b -> ANS(2)b

ANS(2)b b LN1 -5 0 b AN€(2)b

AN€(2)b B LN° -4 -1 b -> AN£2)bb

AN£2)bb 1 LN2 -4 -1 1 w 1 LN2 -4 - ANS(1)


AN.6 ANS(1) b LN1 -5 -1 b -> ANS(1)b

ANS(1)b [-] LN1 -6 0 [-] AN€(1)b

AN€(1)b b LN° -5 -1 b -> AN£1)bb

AN£1)bb b LN2 -5 -1 b w b LN2 -5 - ANS(1)

Q ST IMG N D E A E’ IMG N D DC Q'

04/03/2012 C.G[Texte]

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

Relating to the various stages travelled grids are grouped under the single procedure which

accompanies the course of the analysis.

-Creating a table of identification

-Generalization,

-Aggregation

This is done for the establishment of AN operator to reproduce the analyzed phenomenon, in

the field of observation set: {1, 0, b} {–}.

Grouping

AN.7 ANS(1) [-] LN1 -6 0 [-] -> ANS.cc5

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

AN.8 ANS.cc5 [-] LN1 5 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° 5 +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 5 +1 [-] -> ANS.cc2

AN.8 GXS.cc2 ! +

L Q STQ IMG N D E A E’ IMG N D DC Q'

ANS(1) 1 LN1 0 -1 1 -> ANS(1)1

ANS(1)1 0 LN1 -1 0 0 -> AN€(1)1

AN€(1)1 1 LN° 0 -1 1 -> AN£1)11

AN£1)11 0 LN2 0 -1 0 -> 0 LN1 0 -1 ANS(2)


ANS(2) 0 LN1 -1 -1 0 -> ANS(2)0

ANS(2)0 1 LN1 -2 -1 1 -> AN€(2)0

AN€(2)0 1 LN° -1 -1 1 -> AN£2)01

AN£2)01 0 LN2 -1 -1 0 w 0 LN2 -1 -1 ANS(2)

04/03/2012 C.G[Texte]

The above knowledge grids are gathered around the different categories of States, AN€,

AN£ to which they are referenced.

They allow to identify the phenomenon from the detail of the already observed changes and

thus recognize the actions of an already established operator.


ANS(2) 1 LN1 -2 -1 1 -> ANS(2)1

ANS(2)1 1 LN1 -3 0 1 -> AN€(2)1

AN€(2)1 0 LN° -2 -1 0 -> AN£2)10

AN£2)10 0 LN° -2 -1 0 w 0 LN2 -2 - ANS(2)


ANS(2) 1 LN1 -3 -1 1 -> ANS(2)1

ANS(2)1 b LN1 -4 0 b AN€(2)1

AN€(2)1 1 LN° -3 -1 1 -> AN£2)11

AN£2)11 1 LN2 -3 -1 1 w 1 LN2 -3 - ANS(2)


ANS(2) b LN1 -4 -1 b -> ANS(2)b

ANS(2)b b LN1 -5 0 b AN€(2)b

AN€(2)b b LN° -4 -1 b -> AN£2)bb

AN£2)bb 1 LN2 -4 -1 1 w 1 LN2 -4 - ANS(1)


ANS(1) b LN1 -5 -1 b -> ANS(1)b

ANS(1)b [-] LN1 -6 0 [-] AN€(1)b

AN€(1)b b LN° -5 -1 b -> AN£1)bb

AN£1)bb b LN2 -5 -1 b w b LN2 -5 - ANS(1)

L Q ST IMG N D E A E’ IMG N D DC Q'

ANS(1) [-] LX1 -6 0 [-] -> ANS.cc4

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

GXS.cc2 ! +

04/03/2012 C.G[Texte]

To expand their employment, it returned the data used in the model of the grid.

Table d’identification


ANS(1) 1 LN1 0 -1 1 -> ANS(1)1

ANS(1) b LN1 -5 -1 b -> ANS(1)b

ANS(1) [-] LN1 -6 0 [-] -> ANS.cc5


ANS(1) 1 LN1 n1 -1 1 -> ANS(1)1

ANS(1) b LN1 n1 -1 b -> ANS(1)b

ANS(1) [-] LN1 n1 0 [-] -> ANS.cc5


ANS(1) 1 LN1 0 -1 1 -> ANS(1)1

ANS(1) B LN1 -5 -1 b -> ANS(1)b

ANS(1) [-] LX1 -6 0 [-] -> ANS.cc5

ANS(1)1 0 LN1 -1 0 0 -> AN€(1)1

ANS(1)b [-] LN1 -6 0 [-] AN€(1)b

AN€(1)1 1 LN° 0 -1 1 -> AN£1)11

AN€(1)b B LN° -5 -1 b -> AN£1)bb

AN£1)11 0 LN2 0 -1 0 -> 0 LN2 0 -1 ANS(2)

AN£1)bb B LN2 -5 -1 b w b LN2 -5 -1 ANS(1)


ANS(2) 0 LN1 -1 -1 0 -> ANS(2)0

ANS(2) 1 LN1 -2 -1 1 -> ANS(2)1

ANS(2) 1 LN1 -3 -1 1 -> ANS(2)1

ANS(2) B LN1 -4 -1 b -> ANS(2)b

ANS(2)0 1 LN1 -2 0 1 AN€(2)0

ANS(2)1 1 LN1 -3 0 1 AN€(2)1

ANS(2)1 B LN1 -4 0 b AN€(2)1

ANS(2)b B LN1 -5 0 b AN€(2)b

AN€(2)0 1 LN° -1 -1 1 -> AN£2)01

AN€(2)1 0 LN° -2 -1 0 -> AN£2)10

AN€(2)1 1 LN° -3 -1 1 -> AN£2)11

AN€(2)b B LN° -4 -1 b -> AN£2)bb

AN£2)01 0 LN2 -1 -1 0 w 0 LN2 -1 -1 ANS(2)

04/03/2012 C.G[Texte]

Généralisazion

AN£2)10 0 LN° -2 -1 0 w 0 LN2 -2 -1 ANS(2)

AN£2)11 1 LN2 -3 -1 1 w 1 LN2 -3 -1 ANS(2)

AN£2)bb 1 LN2 -4 -1 1 w 1 LN2 -4 -1 ANS(1)

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

GXS.cc2 ! +


ANS(1) 1 LN1 n1 -1 1 -> ANS(1)1

ANS(1) b LN1 n1 -1 b -> ANS(1)b

ANS(1) [-] LN1 n1 0 [-] -> ANS.cc5

ANS(1)1 0 LN1 n1 0 0 -> AN€(1)1

ANS(1)b [-] LN1 n1 0 [-] -> AN€(1)b

AN€(1)1 1 LN° n° -1 1 -> AN£1)11

AN€(1)b b LN° n° -1 b -> AN£1)bb

AN£1)11 0 LN2 n2 -1 0 w 0 LN1 n2 -1 ANS(2)

AN£1)bb b LN2 n2 -1 b w b LN2 n2 -1 ANS(1)


ANS(2) 0 LN1 n1 -1 0 -> ANS(2)0

ANS(2) 1 LN1 n1 -1 1 -> ANS(2)1

ANS(2) 1 LN1 n1 -1 1 -> ANS(2)1

ANS(2) b LN1 n1 -1 b -> ANS(2)b

ANS(2)0 1 LN1 n1 0 1 AN€(2)0

ANS(2)1 1 LN1 n1 0 1 -> AN€(2)1

ANS(2)1 b LN1 n1 0 b -> AN€(2)1

ANS(2)b b LN1 n1 0 b -> AN€(2)b

AN€(2)0 1 LN° n2 -1 1 -> AN£2)01

AN€(2)1 0 LN° n2 -1 0 -> AN£2)10

AN€(2)1 1 LN° n2 -1 1 -> AN£2)11

AN€(2)b b LN° n2 -1 b -> AN£2)bb

AN£2)01 0 LN2 n2 -1 0 w 0 LN2 -1 -1 ANS(2)

AN£2)10 0 LN2 n2 -1 0 w 0 LN2 -2 -1 ANS(2)

AN£2)11 1 LN2 n2 -1 1 w 1 LN2 -3 -1 ANS(2)

AN£2)bb b LN2 n2 -1 b w 1 LN2 -4 -1 ANS(1)

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

04/03/2012 C.G[Texte]

Aggregation

The experience of several successive learning sweeping digital binary addition possible

configuration would give the full grid is AN operator

Opérateur AN( réduit )

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

GXS.cc2 ! +


ANS(1) 1 LN1 n1 -1 1 -> ANS(1)1

ANS(1) b LN1 n1 -1 b -> ANS(1)b

ANS(1) [-] LN1 n1 0 [-] -> ANS.cc5

ANS(1)1 0 LN1 n1 0 0 -> AN€(1)1

ANS(1)b [-] LN1 n1 0 [-] -> AN€(1)b

AN€(1)1 1 LN° n° -1 1 -> AN£1)11

AN€(1)b b LN° n° -1 b -> AN£1)bb

AN£1)11 0 LN2 n2 -1 0 w 0 LN1 n2 -1 ANS(2)



ANS(2) 0 LN1 n1 -1 0 -> ANS(2)0

ANS(2) 1 LN1 n1 -1 1 -> ANS(2)1

ANS(2) b LN1 n1 -1 b -> ANS(2)b

ANS(2)0 1 LN1 n1 0 1 AN€(2)0

ANS(2)1 1 LN1 n1 0 1 -> AN€(2)1

ANS(2)1 b LN1 n1 0 b -> AN€(2)1

ANS(2)b b LN1 n1 0 b -> AN€(2)b

AN€(2)0 1 LN° n2 -1 1 -> AN£2)01

AN€(2)1 0 LN° n2 -1 0 -> AN£2)10

AN€(2)1 1 LN° n2 -1 1 -> AN£2)11

AN€(2)b b LN° n2 -1 b -> AN£2)bb

AN£2)01 0 LN2 n2 -1 0 w 0 LN2 -1 -1 ANS(2)

AN£2)10 0 LN2 n2 -1 0 w 0 LN2 -2 -1 ANS(2)

AN£2)11 1 LN2 n2 -1 1 w 1 LN2 -3 -1 ANS(2)

AN£2)bb b LN2 n2 -1 b w 1 LN2 -4 -1 ANS(1)

Q STQ IMG N D E A E’ IMG N D DC Q'

ANS(1) 0 LN1 n1 -1 0 -> ANS(1)0

04/03/2012 C.G[Texte]

ANS(1) 1 LN1 n1 -1 1 -> ANS(1)1

ANS(1) b LN1 n1 -1 b -> ANS(1)b

ANS(1) [-] LN1 n1 0 [-] -> ANS.cc5

ANS(1)0 1 LN1 n1 0 1 -> AN€(1)0

ANS(1)1 0 LN1 n1 0 0 -> AN€(1)1

ANS(1)1 1 LN1 n1 0 1 -> AN€(1)1

ANS(1)b [-] LN1 n1 0 [-] -> AN€(1)b

AN€(1)0 0 LN° n° -1 0 -> AN£1)00

AN€(1)0 1 LN° n° -1 1 -> AN£1)01

AN€(1)1 0 LN° n° -1 0 -> AN£1)10

AN€(1)1 1 LN° n° -1 1 -> AN£1)11

AN€(1)b b LN° n° -1 b -> AN£1)bb

AN£1)00 0 LN2 n2 -1 1 w 0 LN2 n2 -1 ANS(1)

AN£1)01 1 LN2 n2 -1 1 w 1 LN2 n2 -1 ANS(1)

AN£1)10 1 LN2 n2 -1 1 w 1 LN2 n2 -1 ANS(1)

AN£1)11 0 LN2 n2 -1 0 w 0 LN2 n2 -1 ANS(2)



ANS(2) 0 LN1 n1 -1 0 -> ANS(2)0

1 LN1 n1 -1 1 -> ANS(2)1

b LN1 n1 -1 b -> ANS(2)b

ANS(2)0 1 LN1 n1 0 1 AN€(2)0

ANS(2)1 1 LN1 n1 0 1 -> AN€(2)1

b LN1 n1 0 b -> AN€(2)1

ANS(2)b b LN1 n1 0 b -> AN€(2)b

AN€(2)1 0 LN° n2 -1 1 -> AN£2)10

1 LN° n2 -1 1 -> AN£2)11

b LN° n2 -1 b -> AN£2)1b

AN€(2)b b LN° n2 -1 b -> AN£2)bb

AN£2)01 0 LN2 n2 -1 0 w 0 LN2 n2 -1 ANS(2)

AN£2)10 0 LN2 n2 -1 0 w 0 LN2 n2 -1 ANS(2)

AN£2)11 1 LN2 n2 -1 1 w 1 LN2 n2 -1 ANS(2)

AN£2)1b 0 LN2 n2 -1 0 w 0 LN2 n2 -1 ANS(2)

AN£2)bb 1 LN2 n2 -1 1 w 1 LN2 n2 -1 ANS(1)

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

GXS.cc2 ! +

04/03/2012 C.G[Texte]

Application of a digital binary addition operator(AN)

ARGUMENTS : 11010+ 1001

n2 : ^

LN2 :

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

The first line of the image of this digital addition

n1 : ^

LN1 : b b 1 1 0 1 0

is postponed on the first line of the grid that corresponds to

AN.1 désigne la première étape de l’analyse qui commence en position zéro par hypothèse

n2 : ^

LN2 :

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

This type of operation does not use the data on the following position. It is registered by the

grid to to maintain its general character.

n2 : ^

LN2 :

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

After the registration of "1" first value of the second argument of this operation on the line

LN °

n° : ^

LN° : b b b 1 0 0 1

It is with AN £ (1) 01 the result of this first step

ANS(1) 0 LN1 n1 -1 0 -> ANS(1)0

AN.1 ANS(1) 0 LN1 0 -1 0 -> ANS(1)0

AN.1 ANS(1)0 1 LN1 -1 0 1 -> AN€(1)0

AN.1 AN€(1)0 1 LN° 0 -1 1 -> AN£1)01

04/03/2012 C.G[Texte]

n2 : ^

LN2 :

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

and the second stage of the analysis

n2 : ^

LN2 :

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1 1

AN.1 AN£1)01 w 1 LN2 n2 -1 ANS(1)

AN.1 ANS(1) 1 LN1 -1 -1 1 -> ANS(1)1

AN.2 ANS(1)1 0 LN1 -2 0 0 -> AN€(1)1

AN.2 AN€(1)1 0 LN° ‚1 -1 0 -> AN£1)10

AN.2 AN£1)10 w 1 LN2 -1 -1 ANS(1)

AN.3 ANS(1) 0 LN1 -2 -1 0 -> ANS(1)0

04/03/2012 C.G[Texte]

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

The corresponding line of the AN operator

AN.3 ANS(1)0 1 LN1 -3 0 1 AN€(1)0

AN.3 AN€(1)0 0 LN° -2 -1 0 -> AN€1)00

AN.3 AN£1)00 w 0 LN2 -2 -1 ANS(1)

AN.4 ANS(1) 1 LN1 -3 -1 1 -> ANS(1)1

AN.4 ANS(1)1 1 LN1 -4 0 1 -> AN€(1)1

AN.4 AN€(1)1 1 LN° -3 -1 1 -> AN£1)11

AN£1)11 0 LN2 n2 -1 0 w 0 LN2 n2 -1 ANS(2)

04/03/2012 C.G[Texte]

which the right-hand side is only active in the use of the operator (the left resumes the results

in learning period repeated use) resulted in a change of index p as indicated by the grid.

n2 : ^

LN2 : 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 :

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

AN.4 AN£1)11 W 0 LN2 -3 -1 ANS(2)

AN.5 ANS(2) 1 LN1 -4 -1 1 -> ANS(2)1

AN.5 ANS(2)1 b LN1 -5 0 b -> AN€(2)1

AN.5 AN€(2)1 b LN° -4 -1 b -> b LN2 -4 ‚1 AN£2)1b

AN.5 AN£2)1b w 0 LN2 -4 -1 ANS(2)

04/03/2012 C.G[Texte]

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

The State AN£ (2) bb on the grid

indicates a new change in the index

n2 : ^

LN2 : 0 0 0 1 1

n° : ^

LN° : b b b 1 0 0 1

n1 : ^

LN1 : b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 0 0 0 1 1

n° : ^

LN° : [] b b b 1 0 0 1

n1 : ^

LN1 : [] b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 0 0 0 1 1

n° : ^

LN° : [] b b b 1 0 0 1

n1 : ^

LN1 : [] b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 0 0 0 1 1

n° : ^

AN.6 ANS(2) B LN1 -5 -1 b -> ANS(2)b

AN.6 ANS(2)b b LN1 -6 0 b -> AN€(2)b

AN.6 AN€(2)b b LN° -5 -1 b -> AN£2)bb

AN£2)bb 1 LN2 n2 -1 1 w 1 LN2 n2 -1 ANS(1)

AN.6 AN£2)bb w 1 LN2 -5 -1 ANS(1)

AN.7 ANS(1) LN1 -6 -1 b -> ANS(1)b

AN.7 ANS(1)b [-] LN1 -7 0 [-] -> AN€(1)b

04/03/2012 C.G[Texte]

LN° : [] b b b 1 0 0 1

n1 : ^

LN1 : [] b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 0 0 0 1 1

n° : ^

LN° : [] b b b 1 0 0 1

n1 : ^

LN1 : [] b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 0 0 0 1 1

n° : ^

LN° : [] b b b 1 0 0 1

n1 : ^

LN1 : [] b b 1 1 0 1 0

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

n2 : ^

LN2 : [] b 1 1 0 0 0

n° : ^

LN° : [] b b 1 0 1 1

n1 : ^

LN1 : [] b b 1 1 0 1

3.B6 AUTOMATON

All the States setting an automaton is obtained by the survey for the following concatenation

and competing events observed A->a->D->e->A->b->C->d

where the transformation of A State is defined by the event met with "a". The State resulting

in the presence of "e" D transforms itself into A………

AN.7 AN€(1)b B LN° -6 -1 b -> AN£1)bb

AN.7 AN£1)bb w b LN2 -6 -1 ANS(1)

AN.8 ANS(1) [-] LN1 -7 0 [-] -> ANS.cc5

ANS.cc5 [-] LN1 n1 +1 [-] -> AN€.cc5

AN€.cc5 [-] LN° n° +1 [-] -> AN£.cc5

AN£.cc5 [-] LN2 n2 +1 [-] -> ANS.cc2

GXS.cc2 ! +

04/03/2012 C.G[Texte]

Analysis grid




[+] LX1 n1 0 [+] -> GXS.cc4

[-] LX1 n1 0 [-] -> GXS.cc5

[/] LX1 n1 0 [/] -> GXS.cc3




GX€(p)i [ ] LX° n° +/- [ ] -> GX£(p)i[]

€j LX° n° +/- €j -> GX£(p)ij

GX€(p)i [ ] LX° n° +/- [ ] -> GXS(p)




[ ] LX2 n2 +/- [ ] -> GXS(p)

GX£(p)ik £k LX2 n2 +/- £k w £k LX2 n2 +/- GX£p)ik



[ ] LX2 n2 +/- [ ] r/w Si LX1 n1 0 GXS(p)



[] LX1 n1 0 [] -> GXS.cc2

GXS.cc2 ! +

GXS.cc3 [/] GX1 n° +1 [/] -> GX€.cc3

04/03/2012 C.G[Texte]

Description of the operator AU

This application describes the evolution of the States of a system from an initial state in view

of the events encountered in the development.

The States are characterized by signs such as {A, B, c} and {a, b, c} events

The original image gives the starting position and the suite of States on the line 1 and of

events observed on the line to °

n2 : ^

AU2 : []

n° : ^

AU° : c a c e b c

n1 : ^

AU1 : C B A E D C

A1 refers to the suite of observed States (CBAEDC)

A1.1 is used to note the first stage of this review

The grid describes the analytical approach by phase in this stage.

The AUS(1) State in the presence of the characteristic sign of the State C transforms into

AUS (1) C and the position of index n1 increase by 1.On this new position of AU1 is the B

sign next stage of our analysis after meeting with the event "c" in the State in AU€ (1) C

GX€.cc3 [] GX° n° +1 [] -> GX£.cc3

GX£.cc3 [] GX2 n2 +1 [] -> GXS.cc2

GXS.cc4 [+] LX1 n1 -1 [+] -> GX€.cc4

GX€.cc4 [+] LX° n° -1 [+] -> GX£.cc4

GX£.cc4 [+] LX2 n2 -1 [+] -> GXS.cc2

GXS.cc5 [-] LX1 n1 +1 [-] -> GX€.cc5

GX€.cc5 [-] LX° n° +1 [-] -> GX£.cc5

GX£.cc5 [-] LX2 n2 +1 [-] -> GXS.cc2

G.E Q STQ IMG N D E Ô E IMG N D DC Q'

A1.1 AUS(1) C AU1 1 +1 C -> AUS(1)C

A1.1 AUS1)C B AU1 2 0 B -> AU€(1)C

A1.1 AU€(1)C c AU° 1 +1 c -> AU£1Cc

A1.1 AU£1Cc [ ] AU2 1 +1 [ ] r/w B AU1 2 0 AUS(1)

04/03/2012 C.G[Texte]

following State AUS (1) C.The spacing found on this position in AU2 product writing B on

AU1 in position 2 (initial position being occupied originally by C).

Unless an anomaly, the chaining of the steps of this kind of way normally loop with the

events met simultaneously with the producted States. However some signs agreed can stop the

process.

DOM : {A,B,C.....,a,b,c} { [ ] }

OPERATEUR : AUTOMATE (AU)

Relevé des changements observés

n2 : ^

AU2 : []

n° : ^

AU° : c a c e b c

n1 : ^

AU1 : C B A E D C

n2 : ^|

AU2 : []

n° : ^ AU° : c a c e b

n1 : ^ AU1 : C B A E D

n2 : ^

AU2 : []

n° : ^ AU° : c a c e b

n1 : ^ AU1 : C B A E D


A1.1 AUS(1) C AU1 1 +1 C -> AUS(1)C

A1.1 AUS1)C B AU1 2 0 B -> AU€(1)C

A1.1 AU€(1)C c AU° 1 +1 C -> AU£1Cc



A1.2 AUS(1) B AU1 2 +1 B -> AUS(1)B

A1.2 AUS(1)B A AU1 3 0 A -> AU€(1)B

A1.2 AU€(1)B a AU° 2 +1 A -> AU£1)Ba

A1.2. AU£1)Ba [ ] AU2 2 +1 [ ] r/w A AU1 3 0 AUS(1)

G.E Q ST IMG N D E A E IMG N D DC Q'

A1.3 AUS(1) A AU1 3 +1 A -> AUS(1)A

A1.3 AUS(1)A E AU1 4 0 E -> AU€(1)A

04/03/2012 C.G[Texte]

n2 : ^

AU2 : []

n° : ^ AU° : c a c e b

n1 : ^ AU1 : C B A E D

n2 : ^

AU2 : []

n° : ^ AU° : c a c e b

n1 : ^ AU1 : C B A E D

n2 :

AU2 :

n° : ^ AU° : c a c e b

n1 : ^ AU1 : C B A E D

Grouping

A1.3 AU€(1)A c AU° 3 +1 C -> AU£(1)Ac

A1.3 AU£(1)Ac [ ] AU2 3 +1 [ ] r/w E AU1 4 0 AUS(1)


A1.4 AUS(1) E AU1 4 +1 A -> AUS(1)E

A1.4 AUS(1)E D AU1 5 0 D -> AU€(1)E

A1.4 AU€(1)E e AU° 4 +1 E -> AU£(1)Ee

A1.4 AU£(1)Ee [ ] AU2 4 +1 [ ] r/w D AU1 5 0 AUS(1)


A1.5 AUS(1) D AU1 5 +1 A -> AUS(1)D

A1.5 AUS(1)D AU1 6 0 D -> --- AU€(1)D

A1.5 AU€(1)D b AU° 5 +1 B -> AU£(1)Db

A1.5 AU£(1)Db [ ] AU2 5 +1 [ ] r/w --- AUS(1)


A1.1 AUS(1) C AU1 1 +1 C -> AUS(1)C

A1.1 AUS1)C B AU1 2 0 B -> AU€(1)C

A1.1 AU€(1)C c AU° 1 +1 c -> AU£1Cc


04/03/2012 C.G[Texte]

Table d’identification


A1.2 AUS(1) B AU1 2 +1 B -> AUS(1)B

A1.2 AUS(1)B A AU1 3 0 A -> AU€(1)B

A1.2 AU€(1)B a AU° 2 +1 a -> AU£1)Ba

A1.2. AU£1)Ba [ ] AU2 2 +1 [ ] r/w A AU1 3 0 AUS(1)


A1.3 AUS(1) A AU1 3 +1 A -> AUS(1)A

A1.3 AUS(1)A E AU1 4 0 E -> AU€(1)A

A1.3 AU€(1)A c AU° 3 +1 c -> AU£(1)Ac

A1.3 AU£(1)Ac [ ] AU2 3 +1 [ ] r/w E AU1 4 0 AUS(1)


A1.4 AUS(1) E AU1 4 +1 A -> AUS(1)E

A1.4 AUS(1)E D AU1 5 0 D -> AU€(1)E

A1.4 AU€(1)E e AU° 4 +1 e -> AU£(1)Ee

A1.4 AU£(1)Ee [ ] AU2 4 +1 [ ] r/w D AU1 5 0 AUS(1)


A1.5 AUS(1) D AU1 5 +1 A -> AUS(1)D

A1.5 AUS(1)D AU1 6 0 -> --- AU€(1)D

A1.5 AU€(1)D b AU° 5 +1 b -> AU£(1)Db

A1.5 AU£(1)Db [ ] AU2 5 +1 [ ] r/w --- AUS(1)


A1.1 AUS(1) C AU1 1 +1 C -> AUS(1)C

A1.2 AUS(1) B AU1 2 +1 B -> AUS(1)B

A1.3 AUS(1) A AU1 3 +1 A -> AUS(1)A

A1.4 AUS(1) E AU1 4 +1 A -> AUS(1)E

A1.5 AUS(1) D AU1 5 +1 A -> AUS(1)D

A1.1 AUS1)C B AU1 2 0 B -> AU€(1)C

A1.2 AUS(1)B A AU1 3 0 A -> AU€(1)B

A1.3 AUS(1)A E AU1 4 0 E -> AU€(1)A

A1.4 AUS(1)E D AU1 5 0 D -> AU€(1)E

A1.5 AUS1)D --- AU1 6 0 D -> AU€(1)D

A1.1 AU€(1)C c AU° 1 +1 c -> AU£1)Cc

04/03/2012 C.G[Texte]

Généralisazion - Aggréga

Opérator AU

In the case of application of the operator, then for each element of the line AU1 can be known

only after the execution of the previous step also reading AUS (1)Si for n1 + 1 is a white []

spacing.

A1.2 AU€(1)B a AU° 2 +1 a -> AU£1)Ba

A1.3 AU€(1)A c AU° 3 +1 c -> AU£1)Ac

A1.4 AU€(1)E e AU° 4 +1 e -> AU£1)Ee

A1.5 AU€(1)D b AU° 5 +1 b -> AU£1Db


A1.2. AU£1Ba [ ] AU2 2 +1 [ ] r/w A AU1 3 0 AUS(1)

A1.3 AU£1Ac [ ] AU2 3 +1 [ ] r/w E AU1 4 0 AUS(1)

A1.4 AU£1Ee [ ] AU2 4 +1 [ ] r/w D AU1 5 0 AUS(1)

A1.5 AU£1Db [ ] AU2 5 +1 [ ] r/w --- AUS(1)


A1.1 AUS(1) Si AU1 n1 +1 Si -> AUS1)Si

A1.1 AUS1)Si SI AU1 n1 0 Si -> AU€(1)Si

A1.1 AU€1)Si €j AU° n° +1 €j -> AU£1)ij

A1.1 AU£1ij [ ] AU2 n2 +1 [ ] r/w Si AU1 n2 0 AUS(1)

Q STQ IMG N D E Ô E IMG N D DC Q'

AUS(1) Si AU1 n1 +1 Si -> AUS1)Si

AUS1)Si [] AU1 n1 0 [] -> AU€(1)Si

AU€1)Si €j AU° n° +1 €j -> AU£1)ij

04/03/2012 C.G[Texte]

7.B 1 REMINDER

THE TURING MACHINE

We describe one of the possible variants of this machine

The basic component of our Turing machine is an infinitely long tape divided lengthwise into

squares. The tape extends in only one direction ( to the right), so that we can meaningfully

talk about “leftmost”square. Each square may contain only one symbol Si from a finite

alphabet {so,…..,sn}. We shall ascribe a special significance of the symbol so : its presence in

a square shall denote that the square is blank . In any tape, the number of nonblank squares is

always finite (but as large as desired), all the other squares being blank.

The second component of the Turing machine is a read-erase-record head. This special device

can move along the tape, either to the left or to the right, one square at a time. Upon an

external command, the head can erase a symbol present in the tape square that happens to face

the head at a given moment, and it can print another one in its stead. The external commands

causing these actions are issued by a controller, a device which is itself governed by the

signals generated by the head (these signals indicate the presence of symbols si in a given tape

square). The controller operates in discrete time (t=0, 1, 2…., and it may assume a finite

number m+1 of internal states qo,…..,Qm. Its input consists of symbols si read and generated by

the head, while its output consists of commands to the head (these commands indicate what

symbol, if any, should be printed in a given tape square, as well as the direction of motion of

the head). For example, assume that at time “t” the head faces the “l”th square from the left,

AU£1ij [ ] AU2 n2 +1 [ ] r/w Si AU1 n2 0 AUS(1)

04/03/2012 C.G[Texte]

that this square contains the symbol si , and that the controller is in state qj . The head reads the

symbol si and generates a signal corresponding to it. In response to this ,the controller

generates a symbol sk which causes the head to erase the old symbol si and print sk on the

tape. Then the controller produces one of the symbols R, L, S (“right”, “left” ,”stop”) ,

incompliance with which the head moves one square to the right or left or stays put. After

this, the controller assumes a new state qr , which is uniquely determined by the previous state

qj and the signal si . After the entire operation has been completed (at time t+1, the “l”th

square contains the symbol sk , the controller is in state qr ,and the head is situated opposite

either the (l+1)st, the (l-1)st, or the “l”th square (depending on whether the motion command

was R, L, or S).

AISERMAN, L.A.GUSEV, L.I.ROZONER, I. MIRNOVA, A. A. TAL’ Logic, Automata,

and Algorithms

8.B1 BIBLIOGRAPHIE

AISERMAN, L.A.GUSEV, L.I.ROZONER, I. MIRNOVA, A. A. TAL’ Logic, Automata, and Algorithms, Academic press, 1971.

P. WATZLAWICK, J.H. BEAVIN, DON D. JACKSON , Une logique de la communication, Edition du seuil, 1972.

R. HERKEN(ed.), The universal Turing Machin a half-century survey, Springer-verlag, 1994.

B.d’ESPAGNAT, C. SALICETI, Candide et le physicien, Fayard, 2008

L.WITTGENSTEIN, Tractatus logico-philosophicus, tel Gallimard, 2009

04/03/2012 C.G[Texte]

the turing machine as a tool for dynamic modeling 2

Documents