Modularity in P Colonies with Checking Rules
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Institute of Computer ScienceSilesian University in Opava
Czech Republic
Modularity in P Colonies with Checking Rules
Luděk Cienciala,Lucie Ciencialová,Miroslav Langer
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Outline
P colonies with capacity one Modularity New results Conclusion
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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
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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
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Rewriting Rules Every agent can change its content by
evolving it
BA
The agent evolves its content by using rewriting rule A B
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Communication Rules Every agent can change its state and
content of environment by communication
AB
Communication is done by using communication rule B A
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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
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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
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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
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
9 AGENTSwithout checking
? AGENTSwith checking
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
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Duplication unit input: object Di output: objects i and i’ requires: one object d contents two agents
ed
e
B1 B2Di
ii’
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
2
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Addition unit input: object Ar output: object ar requires: nothing contents one agent
e
B1
Arar
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
2
1
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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
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Subtraction unit input: object Sr output: object y or object n requires: object ar (if there is any) contents one agent
e
B1
SrBrn
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
2
1
1
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Balance-Wheel unit input: object lh or object e output: object d contents one agent
e
B1
lhedd
e
d
e
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
2
1
1 1
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Control unit Controls computation 4 phases of simulation
1. Initialization2. Simulation of ADD-instruction3. Simulation of SUB-instruction4. Finalization of computation
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Control unit - initialization Generates starting label of
computation of register machine
ed
e
B1 B2e
l0
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Arl2d
Control unit – ADD-instruction l1:(ADD(r),l2,l3)
l1 e
B1 B21’D1
1
Addition unit
Duplication unit
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y
l1:(SUB(r),l2,l3)
l1 el2d
Control unit – SUB-instruction
B1 B21’
D1
1
Subtraction unit
Duplication unit
SrL’1d
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Generates halting label of computation of register machine
lh
Control unit - finalization
de
B1 B2e
Balance-Wheel unit
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
2
1
1
2
12+2+1+1+1=7
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Modules in P ColonyControl unit
Watch balance
Duplication unit
Subtraction unit
Addition unit registers
? AGENTSwith checking
7 AGENTSwith checking
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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,*)
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Thank you all for attention