Event-Related Outputs of Computations in P Systems

Abstract

We briefly investigate the idea to consider as the result of a computation in a P system the number of steps elapsed between two events produced during the computation. Specifically, we first consider the case when the result of a computation is defined in terms of events related to using rules, introducing objects, or meeting objects. Universality is easily obtained in each case for symport/antiport P systems. Then, we address the case when the number computed by a system is the length of a computation itself. We obtain a few results both for catalytic multiset-rewriting and for symport/antiport systems (in each case, also with using membrane dissolution) showing that non-semilinear sets of vectors can be computed in this way. A general non-universality result is proved for this case - no system, of any type, can have as the length of its halting computations all sets of numbers computable by Turing machines. The general problem, of characterizing the sets of numbers computed in this way, remains open.