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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6765097 |
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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. |
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| ISSN: | 1076-2787 1099-0526 |