P systems with elementary active membranes: beyond NP and coNP

Authors:
Antonio E. Porreca;Alberto Leporati;Giancarlo Mauri;Claudio Zandron
Affiliations:
Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milano, Italy;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milano, Italy;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milano, Italy;Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milano, Italy
Venue:
CMC'10 Proceedings of the 11th international conference on Membrane computing
Year:
2010

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Abstract

We prove that a uniform family of P systems with active membranes, where division rules only operate on elementary membranes and dissolution rules are avoided, can be used to solve the following PP-complete decision problem in polynomial time: given a Boolean formula of m variables in 3CNF, do at least √2m among the 2m possible truth assignments satisfy it? As a consequence, the inclusion PP ⊆ PMC AM(-d,-n) holds: this provides an improved lower bound on the class of languages decidable by this kind of P systems.