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 NPcomplete problems. Given a classRof recognizer membrane systems,Rdenotes the set of decision problems solvable by families from R in polynomial time and in a uniform way. PMCR is closed under complement and under polynomial-time reduction. +erefore, if R is a presumably efficient computing model of recognizer membrane systems, then NP ∪ co-NP ⊆PMCR. In this paper, the lower bound NP ∪ co-NP for the time complexity class PMCR is improved for any presumably efficient computing model R of recognizer membrane systems verifying some simple requirements. Specifically, it is shown that DP ∪ co-DP is a lower bound for such PMCR, where DP is the class of differences of any two languages in NP. Since NP ∪ co-NP⊆DP ∩ co- DP, this lower bound for PMCR delimits a thinner frontier than that with NP ∪ co-NP.