Álvaro Romero Jiménez

Complexity classes in models of cellular computing with membranes

In this paper we introduce four complexity classes for cellularcomputing systems with membranes: the first and the second ones containall decision problems solvable in polynomial time by a family ofdeterministic P systems, without and with an input membrane,respectively; the third and fourth classes contain all decision problemssolvable in polynomial time by a family of non-deterministic P systems,without and with an input membrane, respectively. We illustrate theusefulness of these classes by solving two NP–completeproblems, namely HPP and SAT, in both variants of Psystems.

Decision P Systems and the P!=NP Conjecture

We introduce decision P systems, which are a class of P systems with symbol-objects and external output. The main result of the paper is the following: if there exists an NP-complete problem that cannot be solved in polynomial time, with respect to the input length, by a deterministic decision P system constructed in polynomial time, then P ? NP. From Zandron-Ferreti-Mauris theorem it follows that if P ? NP, then no NP-complete problem can be solved in polynomial time, with respect to the input length, by a deterministic P system with active membranes but without membrane division, constructed in polynomial time from the input. Together, these results give a characterization of P ? NP in terms of deterministic P systems

Generation of Diophantine Sets by Computing P Systems with External Output

In this paper a variant of P systems with external output designed to compute functions on natural numbers is presented. These P systems are stable under composition and iteration of functions. We prove that every diophan tine set can be generated by such P systems; then, the universality of this model can be deduced from the theorem by Matiyasevich, Robinson, Davis and Putnam in which they establish that every recursively enumerable set is a diophantine set.