Towards automated deduction in cP systems

Abstract

Inspired by the structure and behaviour of living cells, membrane systems are efficient computing models that can solve NP-complete problems in polynomial time. In this study, we use cP systems to perform automated deduction in equational logic. Using a fixed constant number of generic rewriting rules, our cP solution can perform completion and term reduction efficiently. Given a set of k axioms, the cP system can compute all the critical pairs among the axioms in logarithmic time regardless of k. Even when handling equational theories with n-ary operators, the cP solution’s complexity remains the same. We demonstrate the effectiveness of the approach with a case study. In addition to equational logic, the cP solution can also be used as a prototype to construct deduction cP systems for other logics.