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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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2020, Vol.2020 (2020), p.1-10
Main Authors: Pérez-Hurtado, Ignacio, Martínez-del-Amor, Miguel Á., Orellana-Martín, David, Valencia-Cabrera, Luis, Pérez-Jiménez, Mario J.
Format: Article
Language:English
Subjects:
Completeness
Language
Lower bounds
Membranes
Polynomials
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/6765097