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

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. is closed under complement and under polynomial-time reduction. Therefore, if is a presumably efficient computing model of recognizer membrane systems, then     co - NP     . In this paper, the lower bound     co - NP for the time complexity class is improved for any presumably efficient computing model of recognizer membrane systems verifying some simple requirements. Specifically, it is shown that     co - DP is a lower bound for such , where DP is the class of differences of any two languages in NP . Since     co - NP         co - DP , this lower bound for delimits a thinner frontier than that with     co - NP .