From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
Luis Valencia-Cabrera,
David Orellana-Martín,
Miguel Á. Martínez-del-Amor,
Ignacio Pérez-Hurtado,
Mario J. Pérez-Jiménez
Affiliations
Luis Valencia-Cabrera
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
David Orellana-Martín
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
Miguel Á. Martínez-del-Amor
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
Ignacio Pérez-Hurtado
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
Mario J. Pérez-Jiménez
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain
Presumably efficient computing models are characterized by their capability to provide polynomial-time solutions for NP-complete problems. Given a class ℛ of recognizer membrane systems, ℛ denotes 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. Therefore, 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.
