On Reversibility and Determinism in P Systems

Membrane computing is a formal framework of distributed parallel computing. In this paper we study the reversibility and maximal parallelism of P systems from the computability point of view. The notions of reversible and strongly reversible systems are considered. The universality is shown for reversible P systems with either priorities or inhibitors, and a negative conjecture is stated for reversible P systems without such control. Strongly reversible P systems without control have shown to only generate sub-finite sets of numbers; this limitation does not hold if inhibitors are used. Another concept considered is strong determinism, which is a syntactic property, as opposed to the determinism typically considered in membrane computing. Strongly deterministic P systems without control only accept sub-regular sets of numbers, while systems with promoters and inhibitors are universal.