Institute of Computer ScienceSilesian University in Opava

Czech Republic

Modularity in P Colonies with Checking Rules

Luděk Cienciala,Lucie Ciencialová,Miroslav Langer

Outline

P colonies with capacity one Modularity New results Conclusion

Definition of P Colony The P colony of a capacity 1 with

checking rules is a construct = ( A, e, f, VE, B1, ..., Bn ), where

• A is an alphabet of the P colony• e is an environmental object• f is a final object • VE is an initial content of the environment • B1, ..., Bn are agents living in the P colony

Definition of P Colony Agent Bi is a touple

1. An initial content of the agent (multiset of only one object)

2. A set of programs (each program is formed from onle rule)

Three types of rules:1. Rewriting2. Communication 3. Checking

Rewriting Rules Every agent can change its content by

evolving it

BA

The agent evolves its content by using rewriting rule A B

Communication Rules Every agent can change its state and

content of environment by communication

AB

Communication is done by using communication rule B A

Checking rules Not really new type, it set “priority”

between two rules.

AB

Checking rule is formed from two rules for example

A B/A C

Checking rules Not really new type, it set “priority”

between rules.

AB

Checking rule is formed from two rules for example

A B/A C

C

Computation A computation is done in maximally

parallel way The maximal number of working

agents Computation ends by halting A result is the number of copies of

final object f placed in the environment at the end of computation

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

9 AGENTSwithout checking

? AGENTSwith checking

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

Duplication unit input: object Di output: objects i and i’ requires: one object d contents two agents

ed

e

B1 B2Di

ii’

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

2

Addition unit input: object Ar output: object ar requires: nothing contents one agent

e

B1

Arar

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

2

1

Subtraction unit input: object Sr output: object y or object n requires: object ar (if there is any) contents one agent

e

B1

Sr

ar

Bry

Subtraction unit input: object Sr output: object y or object n requires: object ar (if there is any) contents one agent

e

B1

SrBrn

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

2

1

1

Balance-Wheel unit input: object lh or object e output: object d contents one agent

e

B1

lhedd

e

d

e

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

2

1

1 1

Control unit Controls computation 4 phases of simulation

1. Initialization2. Simulation of ADD-instruction3. Simulation of SUB-instruction4. Finalization of computation

Control unit - initialization Generates starting label of

computation of register machine

ed

e

B1 B2e

l0

Arl2d

Control unit – ADD-instruction l1:(ADD(r),l2,l3)

l1 e

B1 B21’D1

1

Addition unit

Duplication unit

y

l1:(SUB(r),l2,l3)

l1 el2d

Control unit – SUB-instruction

B1 B21’

D1

1

Subtraction unit

Duplication unit

SrL’1d

Generates halting label of computation of register machine

lh

Control unit - finalization

de

B1 B2e

Balance-Wheel unit

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

2

1

1

2

12+2+1+1+1=7

Modules in P ColonyControl unit

Watch balance

Duplication unit

Subtraction unit

Addition unit registers

? AGENTSwith checking

7 AGENTSwith checking

Results NPCOLmparK(1,*,5) = NRE NPCOLmpar K(1,3,*) =

NRE

NPCOLmparK(1,*,7) = NRE NPCOLmpar K(1,4,*) =

NRE NPCOLmpar (1,4,*) = NRE NRMpb NPCOL

mpar(1,2,*)

Thank you all for attention