P colonies with agent division

P colonies, a variant of membrane (P) systems, are simple cell-inspired multi-agent systems without an inner structure of agents. The agents consist of a single membrane with a fixed number of atomic objects inside. Yet, they have interesting computational properties thanks to the collaboration and coordination of agents. Certain types of P colonies have been previously shown to be computationally complete in the Turing sense. We introduce a new type of rules for P colonies, inspired by the process of cell fission (division). We show that these extended P colonies can deterministically solve the Problem 3-SAT in linear time with respect to the number of clauses of the formula, starting with three agents only. In turn, classes NP and co-NP are solvable in polynomial time by polynomially uniform families of these P colonies. Several open problems arise, among others the possibility of characterization of the borderline between P and NP by certain parameters of P colonies. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

P-networks are simple multi-agent systems with interesting computational properties. We introduce new rules for P-networks and demonstrate their potential in problem-solving.