Time-Free Solution to 3-Coloring Problem Using Tissue P Systems

P systems withd-division are a particular class of distributed and parallel computing models investigated in membrane computing, which are inspired from the budding behavior of Baker’s yeast (a cell can generate several cells in one reproducing cycle). In previous works, such systems can theoretically generate exponential working space in linear time and thus provide a way to solve computational hard problems in polynomial time by a space-time tradeoff, where the precise execution time of each evolution rule, one time unit, plays a crucial role. However, the restriction that each rule has a precise same execution time does not coincide with the biological fact, since the execution time of biochemical reactions can vary because of external uncontrollable conditions. In this work, we consider timed P systems withd-division by adding a time mapping to the rules to specify the execution time for each rule, as well as the efficiency of the systems. As a result, a time-free solution to Hamiltonian path problem (HPP) is obtained by a family of such systems (constructed in a uniform way), that is, the execution time of the rules (specified by different time mappings) has no influence on the correctness of the solution.

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Time-Free Solution to SAT Problem by Tissue P Systems

Mathematical Problems in Engineering ◽

10.1155/2017/1567378 ◽

2017 ◽

Vol 2017 ◽

pp. 1-8 ◽

Cited By ~ 3

Author(s):

Yueguo Luo ◽

Zhongyang Xiong ◽

Guanghua Zhang

Keyword(s):

Intercellular Communication ◽

Execution Time ◽

Efficient Solution ◽

Point Of View ◽

P Systems ◽

Free Solution ◽

Complete Problem ◽

Np Complete ◽

First Time ◽

Computing Models

Tissue P systems are a class of computing models inspired by intercellular communication, where the rules are used in the nondeterministic maximally parallel manner. As we know, the execution time of each rule is the same in the system. However, the execution time of biochemical reactions is hard to control from a biochemical point of view. In this work, we construct a uniform and efficient solution to the SAT problem with tissue P systems in a time-free way for the first time. With the P systems constructed from the sizes of instances, the execution time of the rules has no influence on the computation results. As a result, we prove that such system is shown to be highly effective for NP-complete problem even in a time-free manner with communication rules of length at most 3.

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Time-Free Solution for QSAT by Using Timed Tissue P Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.568-570.812 ◽

2014 ◽

Vol 568-570 ◽

pp. 812-816 ◽

Cited By ~ 1

Author(s):

Yun Yun Niu ◽

Zhi Gao Wang

Keyword(s):

Computational Efficiency ◽

Execution Time ◽

Realistic Model ◽

Point Of View ◽

P Systems ◽

P System ◽

Free Solution ◽

Complete Problem ◽

Computational Processes ◽

Tissue P System

A timed tissue P system is constructed by adding a time mapping to the rules of tissue P system to specify the execution time for each rule. It is a more realistic model from a biological point of view. In this study, we investigate the computational efficiency of timed tissue P systems. A uniform and time-free solution to QSAT problem, a famous PSPACE-complete problem, is proposed, where the execution time of the computational processes involved can vary arbitrarily and the output produced is always the same.

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Time-free solution to SAT problem using P systems with active membranes

Theoretical Computer Science ◽

10.1016/j.tcs.2013.11.014 ◽

2014 ◽

Vol 529 ◽

pp. 61-68 ◽

Cited By ~ 32

Author(s):

Tao Song ◽

Luis F. Macías-Ramos ◽

Linqiang Pan ◽

Mario J. Pérez-Jiménez

Keyword(s):

P Systems ◽

Free Solution ◽

Sat Problem ◽

Active Membranes

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Time-free solution to SAT problem by P systems with active membranes and standard cell division rules

Natural Computing ◽

10.1007/s11047-014-9471-4 ◽

2014 ◽

Vol 14 (4) ◽

pp. 673-681 ◽

Cited By ~ 17

Author(s):

Bosheng Song ◽

Tao Song ◽

Linqiang Pan

Keyword(s):

Cell Division ◽

P Systems ◽

Standard Cell ◽

Free Solution ◽

Sat Problem ◽

Active Membranes

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Time-free Solution to Independent Set Problem using P Systems with Active Membranes

Fundamenta Informaticae ◽

10.3233/fi-2021-2072 ◽

2021 ◽

Vol 182 (3) ◽

pp. 243-255

Author(s):

Yu Jin ◽

Bosheng Song ◽

Yanyan Li ◽

Ying Zhu

Keyword(s):

Membrane Computing ◽

Independent Set ◽

P Systems ◽

Natural Computing ◽

Free Solution ◽

Independent Set Problem ◽

Global Clock ◽

Active Membranes ◽

Biological Reality ◽

Hard Problems

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problem using P systems with active membranes, which solve the problem independent of the execution time of the involved rules.

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