The P Versus NP Problem Through Cellular Computing with Membranes

Pérez–Jiménez, Mario J.; Romero–Jiménez, Álvaro; Sancho-Caparrini, Fernando

doi:10.1007/978-3-540-24635-0_26

Cited by 29 publications

(30 citation statements)

References 4 publications

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“…This class is closed under polynomial-time reduction and under complement (see [13] for a similar result for cell-like P systems). We also denote by PMC T D(k) the set of all decision problems which can be solved by means of recognizer tissue P systems with cell division in polynomial time, by using communication rules whose length is, at most, k.…”

Section: Polynomial Solvability By Recognizer Tissue P Systemsmentioning

confidence: 78%

Characterizing Tractability by Tissue-Like P Systems

Gutiérrez–Escudero

Pérez–Jiménez

Rius-Font

2010

Lecture Notes in Computer Science

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Summary. In the framework of cell-like membrane systems it is well known that the construction of exponential number of objects in polynomial time is not enough to efficiently solve NP-complete problems. Nonetheless, it may be sufficient to create an exponential number of membranes in polynomial time. In the framework of recognizer polarizationless P systems with active membranes, the construction of an exponential workspace expressed in terms of number of membranes and objects may not suffice to efficiently solve computationally hard problems.In this paper we study the computational efficiency of recognizer tissue P systems with communication (symport/antiport) rules and division rules. Some results have been already obtained in this direction: (a) using communication rules and forbidding division rules, only tractable problems can be efficiently solved; (b) using communication rules with length three and division rules, NP-complete problems can be efficiently solved. In this paper we show that the allowed length of communication rules plays a relevant role from the efficiency point of view of the systems.

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Section: Polynomial Solvability By Recognizer Tissue P Systemsmentioning

confidence: 78%

Characterizing Tractability by Tissue-Like P Systems

Gutiérrez–Escudero

Pérez–Jiménez

Rius-Font

2010

Lecture Notes in Computer Science

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“…In the framework of AM(−n), efficient uniform solutions to weakly NPcomplete problems (Knapsack [27], Subset Sum [26], Partition [10]), and strongly NP-complete problems (SAT [32], Clique [4], Bin Packing [30], Common Algorithmic Problem [29]) have been obtained.…”

Section: Proposition 4 (Milano Theorem)mentioning

confidence: 99%

A Computational Complexity Theory in Membrane Computing

Pérez–Jiménez

2010

Membrane Computing

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Summary. In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented. Many attractive characterizations of P = NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.

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“…For a clearer description of the difference between uniform P systems and semi-uniform P systems, please refer to [7].…”

Section: P Systemsmentioning

confidence: 99%