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 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...

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Main Authors: Luis Valencia-Cabrera, David Orellana-Martín, Miguel Á. Martínez-del-Amor, Ignacio Pérez-Hurtado, Mario J. Pérez-Jiménez
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/6765097
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author Luis Valencia-Cabrera
David Orellana-Martín
Miguel Á. Martínez-del-Amor
Ignacio Pérez-Hurtado
Mario J. Pérez-Jiménez
author_facet Luis Valencia-Cabrera
David Orellana-Martín
Miguel Á. Martínez-del-Amor
Ignacio Pérez-Hurtado
Mario J. Pérez-Jiménez
author_sort Luis Valencia-Cabrera
collection DOAJ
description 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.
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spelling doaj-art-b4818bce4dc344518deae5cec7ef020f2025-08-20T02:23:12ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/67650976765097From NP-Completeness to DP-Completeness: A Membrane Computing PerspectiveLuis Valencia-Cabrera0David Orellana-Martín1Miguel Á. Martínez-del-Amor2Ignacio Pérez-Hurtado3Mario J. Pérez-Jiménez4Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainResearch Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainResearch Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainResearch Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainResearch Group on Natural Computing, Department of Computer Science and Artificial Intelligence, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, SpainPresumably 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.http://dx.doi.org/10.1155/2020/6765097
spellingShingle Luis Valencia-Cabrera
David Orellana-Martín
Miguel Á. Martínez-del-Amor
Ignacio Pérez-Hurtado
Mario J. Pérez-Jiménez
From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
Complexity
title From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
title_full From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
title_fullStr From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
title_full_unstemmed From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
title_short From NP-Completeness to DP-Completeness: A Membrane Computing Perspective
title_sort from np completeness to dp completeness a membrane computing perspective
url http://dx.doi.org/10.1155/2020/6765097
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