Modularity in P-Colonies with Checking Rules: New Findings and Computation Analysis
This paper analyzes P-colonies with capacity one, exploring new modularity results. A P-colony consists of agents that interact with an environment, using rewriting, communication, and checking rules to evolve their content. Our research defines how these agents compute through parallel processes, focusing on the structure of their control units and operational modules. We detail computation phases such as initialization, ADD and SUB instruction simulations, and the finalization of processes. The results show various non-recursive (NRE) complexity cases related to the configurations of agents and rules.
Modularity in P-Colonies with Checking Rules: New Findings and Computation Analysis
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Modularity in P ColonieswithCheckingRules Luděk Cienciala,Lucie Ciencialová,Miroslav Langer • Institute of Computer Science • Silesian University in Opava • CzechRepublic
Outline P colonieswithcapacityone Modularity New results Conclusion
Definition of P Colony • The P colony of a capacity 1withcheckingrulesisa construct = ( A, e, f, VE, B1, ..., Bn), where • A is an alphabet ofthe P colony • e is an environmental object • f is a final object • VEis an initial content of the environment • B1, ..., Bnare agents living in the P colony
Definitionof P Colony • Agent Bi is a touple • Aninitialcontentofthe agent (multiset ofonlyoneobject) • A set ofprograms (each program isformedfromonle rule) • Three types ofrules: • Rewriting • Communication • Checking
RewritingRules B A The agent evolves its content by usingrewriting ruleA B Every agent can change its content by evolving it
CommunicationRules B A Communication is done by usingcommunication ruleBA Every agent can change its state and content of environment by communication
Checkingrules A B Checking ruleis formed from two rules for example A B/A C Not really new type, it set “priority” between two rules.
Checkingrules A C B Checking ruleis formed from two rules for example A B/A C Not really new type, it set “priority” between rules.
Computation A computation is done in maximally parallel way The maximal number of working agents Computationends 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 Colony 9 AGENTS without checking ? AGENTS with checking Control unit Duplication unit Watch balance Subtraction unit Addition unit registers
Modules in P Colony Control unit Duplication unit Watch balance Subtraction unit Addition unit registers
Duplication unit Di B1 B2 i’ i e e d input: object Di output: objects i and i’ requires: one object d contents two agents
Modules in P Colony Control unit 2 Duplication unit Watch balance Subtraction unit Addition unit registers
Addition unit B1 Ar ar e input: object Ar output: objectar requires: nothing contents one agent
Modules in P Colony Control unit 2 Duplication unit Watch balance Subtraction unit Addition unit registers 1
Subtraction unit ar B1 Sr y Br e input: object Sr output: objectyorobjectn requires: objectar (ifthereisany) contents one agent
Subtraction unit B1 Sr n Br e input: object Sr output: objectyorobjectn requires: objectar (ifthereisany) contents one agent
Modules in P Colony Control unit 2 Duplication unit Watch balance Subtraction unit 1 Addition unit registers 1
Balance-Wheel unit e e B1 e lh d e d d input: object lhorobjecte output: objectd contents one agent
Modules in P Colony Control unit 2 Duplication unit Watch balance 1 Subtraction unit 1 Addition unit registers 1
Control unit • Controlscomputation • 4 phasesofsimulation • Initialization • Simulationof ADD-instruction • Simulationof SUB-instruction • Finalizationofcomputation
Control unit - initialization e B1 B2 e l0 e d Generatesstartinglabelofcomputationofregistermachine
Control unit – ADD-instruction Addition unit 1’ 1 B1 B2 Ar D1 l1 l2 e d Duplication unit l1:(ADD(r),l2,l3)
Control unit – SUB-instruction Subtraction unit 1 B1 B2 1’ y l1 Sr D1 L’1 d e l2 d Duplication unit l1:(SUB(r),l2,l3)
Control unit - finalization e B1 B2 lh e d Balance-Wheel unit Generateshaltinglabelofcomputationofregistermachine
Modules in P Colony 2 Control unit 2 Duplication unit 2+2+1+1+1=7 Watch balance 1 Subtraction unit 1 Addition unit registers 1
Modules in P Colony 7 AGENTS with checking ? AGENTS with checking Control unit Duplication unit Watch balance Subtraction unit Addition unit registers
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,*)
