Simulating counting oracles with cooperation

Abstract

Many variants of P systems with active membranes are able to solve traditionally intractable problems. Sometimes they also characterize well known complexity classes, depending upon the computational features they use. In this paper we continue the investigation of the importance of (minimal) cooperative rules to increase the computational power of P systems. In particular, we prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise $$\mathbf{P }^{\#{\mathbf{P }}}_{\parallel }$$ , the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem.