Solving a PSPACE-complete Problem with cP Systems

Abstract

There have been a few NP-hard problems solved using cP systems including the travelling salesman problem. However, these problems are typically in NP rather than higher in the polynomial time hierarchy. In this paper we solve QSAT (also known as TQBF), which is a well-known PSPACE-complete problem. Compared to other extant confluent P systems solutions, our deterministic cP solution only uses a small constant number of custom alphabet symbols (19), a small constant number of rules (10), and a small constant upper-limit of membrane nesting depth (6), independent of the problem size.