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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| 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. |
| format | Article |
| id | doaj-art-b4818bce4dc344518deae5cec7ef020f |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| 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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