A Linear‐Time Solution for All‐SAT Problem Based on P System

Guo, Ping; Zhu, Jian; Chen, Haizhu; Yang, Ruilong

doi:10.1049/cje.2018.01.008

Cited by 9 publications

(4 citation statements)

References 11 publications

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“…At present, many new variants have been proposed [3][4][5][6][7][8][9], and many variants have been proven Turing universal. In the theoretical research of membrane computing, various computationally hard problems were solved [10][11][12][13][14]. Recently, inspired by membrane computing, Roy et al proposed a new type of neural computing system [15], which will promote the development of membrane computing.…”

Section: Introductionmentioning

confidence: 99%

Solving the SAT Problem by Cell-Like P Systems with Channel States and Symport Rules

Wan

Liu

Yue-guo

2023

Discrete Dynamics in Nature and Society

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Cell-like P systems with channel states, which are a variant of tissue P systems in membrane computing, can be viewed as highly parallel computing devices based on the nested structure of cells, where communication rules are classified as symport rules and antiport rules. In this work, we remove the antiport rules and construct a novel variant, namely, cell-like P systems with channel states and symport rules, where one rule is only allowed to be nondeterministically applied once per channel. To explore the computational efficiency of the variant, we solve the S A T problem and obtain a uniform solution in polynomial time with the maximal length of rules 1. The results of our work are reflected in the following two aspects: first, communication rules are restricted to only one type, namely, symport rules; second, the maximal length of rules is decreased from 2 to 1. Our work indicates that the constructed variant with fewer rule types can still solve the S A T problem and obtain better results in terms of computational complexity. Hence, in terms of computational efficiency, our work is a notable improvement.

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Section: Introductionmentioning

confidence: 99%

Solving the SAT Problem by Cell-Like P Systems with Channel States and Symport Rules

Wan

Liu

Yue-guo

2023

Discrete Dynamics in Nature and Society

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“…Currently, a variety of membrane systems are Turing universal [4], [5], [6], [7], [8], [9]. Relative to computational efficiency, various variants are applied to solve NP-hard problems, such as the SAT problem [10], [11], vertex cover problem [12] and the 3-coloring problem [13], [14]. In addition, arithmetic operations [15], [16] and logical expressions [17] have been solved theoretically.…”

Section: Introductionmentioning

confidence: 99%

Flip-flop P systems with proteins on membranes in a time-free manner

2023

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Flip-flop P systems with proteins are a bio-inspired variant of cell-like P systems in membrane computing, where proteins can control the execution of rules. In this work, firstly, in order to simulate the fact that the execution time of biochemical reactions is uncertain, considering time-freeness, we therefore construct a novel variant, namely timed flip-flop P systems with proteins, where the protein on each membrane only has two types of working states, and such a system runs under the time-freeness mode; secondly, we study the computation power of this variant, and it is shown that a system with only one membrane and a maximum rule length of 4 is Turing universal; moreover, based on the variant, a solution to the SAT problem is obtained by the constructed system in polynomial time. Our work indicates that the constructed variant with time-freeness can still solve the SAT problem in feasible time. Because timefreeness of rules is employed, the variant may be more suitable for particular applications. INDEX TERMS P system, protein, university, SAT , time-freeness.

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“…The distributed parallel computing models obtained from the development of membrane computing are membrane systems, also known as P systems, and the study of P systems has been divided into three types according to the cell membrane structure or cell distribution: cell-like P systems, tissue-like P systems, and neural-like P systems. For the theoretical research of membrane computing, three types of P systems have been extended to obtain several universal computational models [ 3 , 4 , 5 , 6 , 7 ], and the computational complexity of extended P systems has been explored [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. For the application research of membrane computing, existing studies have realized the integration of membrane computing with algorithms for applications in robot control [ 21 , 22 ], data modeling, and optimization [ 23 , 24 , 25 , 26 ], algorithms for solving NP problems [ 27 , 28 , 29 ], clustering algorithms [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ], and image processing [ 38 , 39 , 40 ].…”

Section: Introductionmentioning

confidence: 99%

Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes

Liu

Zhao

2022

Entropy

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Spiking neural P systems (SN P systems for short) realize the high abstraction and simulation of the working mechanism of the human brain, and adopts spikes for information encoding and processing, which are regarded as one of the third-generation neural network models. In the nervous system, the conduction of excitation depends on the presence of membrane potential (also known as the transmembrane potential difference), and the conduction of excitation on neurons is the conduction of action potentials. On the basis of the SN P systems with polarizations, in which the neuron-associated polarization is the trigger condition of the rule, the concept of neuronal membrane potential is introduced into systems. The obtained variant of the SN P system features charge accumulation and computation within neurons in quantity, as well as transmission between neurons. In addition, there are inhibitory synapses between neurons that inhibit excitatory transmission, and as such, synapses cause postsynaptic neurons to generate inhibitory postsynaptic potentials. Therefore, to make the model better fit the biological facts, inhibitory rules and anti-spikes are also adopted to obtain the spiking neural P systems with membrane potentials, inhibitory rules, and anti-spikes (referred to as the MPAIRSN P systems). The Turing universality of the MPAIRSN P systems as number generating and accepting devices is demonstrated. On the basis of the above working mechanism of the system, a small universal MPAIRSN P system with 95 neurons for computing functions is designed. The comparisons with other SN P models conclude that fewer neurons are required by the MPAIRSN P systems to realize universality.

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A Linear‐Time Solution for All‐SAT Problem Based on P System

Cited by 9 publications

References 11 publications

Solving the SAT Problem by Cell-Like P Systems with Channel States and Symport Rules

Solving the SAT Problem by Cell-Like P Systems with Channel States and Symport Rules

Flip-flop P systems with proteins on membranes in a time-free manner

Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes

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