Decidability of Divergence for Catalytic P Systems

Abstract

P systems are a biologically inspired model introduced by Gheorghe P¸aun with the aim of representing the structure and the functioning of the cell. Since their introduction, several variants of P systems have been proposed and explored. We concentrate on the class of catalytic P systems without priorities associated to the rules. We show that the divergence problem (i.e., checking for the existence of an infinite computation) is decidable in such a class of P systems. As a corollary, we obtain an alternative proof of the nonuniversality of deterministic catalytic P systems, an open problem recently solved by Ibarra and Yen.