applications of the matrix model of computation sergio pissanetzky
DESCRIPTION
The MMC is universal ●Software Engineering Object-oriented analysis and design. Object-oriented refactoring. Software development. ●Physics SCA algorithm, ontologies. From thought experiments to theories. ●Business Business applications of the MMC. ●UML MMC applications to UML models. Inheritance, polymorphism. ●Artificial Intelligence Neural networks, parallelism, training, dynamics.TRANSCRIPT
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Applications of theMatrix Model of Computation
Sergio Pissanetzky
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The MMC consists of two sparse matrices: M = (C, Q) C = Matrix of Services Q = Matrix of Sequences
The model has two forms: ● imperative form
● canonical form. Matrix Q is the imperative part of the model.
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The MMC is universal● Software Engineering
Object-oriented analysis and design.Object-oriented refactoring.Software development.
● PhysicsSCA algorithm, ontologies.From thought experiments to theories.
● BusinessBusiness applications of the MMC.
● UMLMMC applications to UML models.Inheritance, polymorphism.
● Artificial IntelligenceNeural networks, parallelism, training, dynamics.
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A
B
C
A Business Problem
M
S
Services: Init, AM, BM, CM, AS, BS, CS, MCost, SCost
b a
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actor P a b F 1 init
init M A AM init M B BM init M C CM init S A AS init S B BS init S C CS AM MCost BM MCost CM MCost AS SCost BS SCost CS SCost MCost exit SCost exit
Matrix of Sequences
R
Q =
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P a b Finit M A AMinit M B BMinit M C CMinit S A ASinit S B BSinit S C CS
Relation R =
Program in C if(a==M && b==A) AM;if(a==M && b==B) BM;if(a==M && b==C) CM;if(a==S && b==A) AS;if(a==S && b==B) BS;if(a==S && b==C) CS;
Relations are code
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Relations are object-orientedP a b F
init M A AMinit M B BMinit M C CMinit S A ASinit S B BSinit S C CS
Relation R =
MMC OO Model relation inheritance hierarchy
control variable base classeach allowed value derived class
sub-relation virtual method
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P a k b Finit M 1 A AMinit M 1 B BMinit M 1 C CMinit S 2 A ASinit S 2 B BSinit S 2 C CS
R =
Relations support inheritance transformations
P a b Finit M 1init S 21 A AM1 B BM1 C CM2 A AS2 B BS2 C CS
R1
R2
Transformation Relational operationmultiple to single normalization, projectionsingle to multiple join
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P a h b Finit M 3 A AMinit M 4 B BMinit M 5 C CMinit S 3 A ASinit S 4 B BSinit S 5 C CS
R =
● Consider control variable b.● Add foreign keys for variable b.● Project on (P, b, h) and (h, a, F).
P a b Finit A 3init B 4init C 53 M AM3 S AS4 M BM4 S BS5 M CM5 S CS
R3
R4
Case b/a
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P a b Finit M 1init S 21 A AM1 B BM1 C CM2 A AS2 B BS2 C CS
AM MCost BM MCost CM MCost AS SCost BS SCost CS SCost
MCost exitSCost exit
Document
Cost(a)MListSList
AModelMList{AM}SList{AS}
BModelMList{BM}SList{BS}
CModelMList{CM}SList{CS}
MailMCost(Document d)
SpraySCost(Document d)
R1
R2
Relations support UML models
Caller initializes a.Caller constructs A/B/CModel initialize b.Caller calls Cost, passing aCost selects MList /SList a decision.MList, SList call their override b decision,calculate the list of equipment,construct a Mail or Spray object,and call their M/SCost method to calculate cost.
R2
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Documentaccept(Visitor v)
AModelaccept(Visitor v){v.visitA(this)}
BModelaccept(Visitor v){v.visitB(this)}
CModelaccept(Visitor v){v.visitC(this)}
MailvisitA(AModel d){AM}visitB(BModel d){BM}visitC(CModel d){CM}
SprayvisitA(AModel d){AS}visitB(BModel d){BS}visitC(CModel d){CS}
VisitorvisitA(AModel d)visitB(BModel d)visitC(CModel d)
Relations support Patterns
R3
R4
P a b Finit A 3init B 4init C 53 M AM3 S AS4 M BM4 S BS5 M CM5 S CS
AM MCost BM MCost CM MCost AS SCost BS SCost CS SCost
MCost exitSCost exit
R3
R4
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Action Traditional method MMC
decide what to refactor manual automatic
perform the refactoring
manual (tools available for some languages) automatic
procedure 16 Fowler refactorings 1 normalization
implementation requires use of pattern natural
Refactoring in the MMC
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Conclusions
● The MMC is Universal
● Interfaces easily with applications
● Supports Object-Orientation
● Unifying factor for systems