From NP-Completeness to DP-Completeness: A Membrane Computing Perspective

Abstract

Presumably efficient computing models are characterized by their capability to provide polynomial-time solutions for NP-complete problems. Given a class of recognizer membrane systems, denotes the set of decision problems solvable by families from in polynomial time and in a uniform way. PMC is closed under complement and under polynomial-time reduction. Therefore, if is a presumably efficient computing model of recognizer membrane systems, then NP ∪ co-NP ⫅ PMC. In this paper, the lower bound NP ∪ co-NP for the time complexity class PMC is improved for any presumably efficient computing model of recognizer membrane systems verifying some simple requirements. Specifically, it is shown that DP ∪ co-DP is a lower bound for such PMC, where DP is the class of differences of any two languages in NP. Since NP ∪ co-NP ⫅ DP ∩ co-DP, this lower bound for PMC delimits a thinner frontier than that with NP ∪ co-NP.