P colonies and prescribed teams

Abstract

We further investigate the computational power of P colonies working in the maximally parallel and sequential modes. It turns out that there is a trade-off between maximal parallelism and checking programs: using checking programs (i.e. priorities on the communication rules in the programs of the agents), P colonies working in the sequential mode with a height of at most five are computationally complete, whereas when working in the maximally parallel mode, P colonies (again with height five) already obtain the same computational power without using checking programs. Moreover, when allowing an arbitrary number of programs for each agent, we can prove that P colonies with only one agent (thus these P colonies are working in the sequential mode) are already computationally complete. On the other hand, P colonies with an arbitrary number of agents working in the sequential mode, as well as even P colonies with only one agent using an arbitrary number of non-checking programs, characterize the family of Parikh sets generated by matrix grammars without appearance checking. The completeness results can also be obtained for P colonies with prescribed teams where rules work in parallel at each agent. P colonies with prescribed teams working in the t 0 mode yield computational completeness even with one agent without priorities on the teams. On the other hand, the family of Parikh sets generated by matrix grammars without appearance checking is also characterized by P colonies with prescribed teams consisting of only (at most) two sets containing exactly one evolution rule or one antiport rule when working in the modes *,=1,≥1, and ≤ k for k ≥1, in one or an arbitrary number of agents.