Multisets are the fundamental data structure of P systems. In this paper we relate P systems with the language and theory for multisets presented in [9.] This allows us, on the one hand, to define and implement P systems using multiset constraints in a constraint logic programming framework, and, on the other hand, to define and implement constraint solving procedures used to test multiset constraint satisfiability in terms of P systems with active membranes. While the former can be exploited to provide a precise formulation of a P system, as well as a working implementation of it, based on a first-order theory, the latter provides a way to obtain a P system for a given problem (in particular, NP problems) starting from a rather natural encoding of its solution in terms of multiset constraints.
