A Uniform Solution to Subset Sum by Tissue P Systems with Cell Separation

Tissue P systems are a class of bio-inspired computing models motivated by biochemical interactions between cells in a tissue-like arrangement. Tissue P systems with cell division offer a theoretical device to generate an exponentially growing structure in order to solve computationally hard problems efficiently with the assumption that there exists a global clock to mark the time for the system, the execution of each rule is completed in exactly one time unit. Actually, the execution time of different biochemical reactions in cells depends on many uncertain factors. In this work, with this biological inspiration, we remove the restriction on the execution time of each rule, and the computational efficiency of tissue P systems with cell division is investigated. Specifically, we solve subset sum problem by tissue P systems with cell division in a time-free manner in the sense that the correctness of the solution to the problem does not depend on the execution time of the involved rules.

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Solving 3-coloring problem by tissue P systems with cell separation

2009 Fourth International on Conference on Bio-Inspired Computing ◽

10.1109/bicta.2009.5338122 ◽

2009 ◽

Author(s):

Shuo Wang ◽

Zhengke Miao ◽

Xiaolong Shi ◽

Zheng Zhang

Keyword(s):

Cell Separation ◽

P Systems ◽

Coloring Problem

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The Efficiency of Tissue P Systems with Cell Separation Relies on the Environment

Membrane Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-36751-9_17 ◽

2013 ◽

pp. 243-256 ◽

Cited By ~ 8

Author(s):

Luis F. Macías-Ramos ◽

Mario J. Pérez-Jiménez ◽

Agustín Riscos-Núñez ◽

Miquel Rius-Font ◽

Luis Valencia-Cabrera

Keyword(s):

Cell Separation ◽

P Systems

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Tissue P Systems with Cell Separation: Upper Bound by PSPACE

Theory and Practice of Natural Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-33860-1_17 ◽

2012 ◽

pp. 201-215 ◽

Cited By ~ 1

Author(s):

Petr Sosík ◽

Luděk Cienciala

Keyword(s):

Upper Bound ◽

Cell Separation ◽

P Systems

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The Computational Complexity of Tissue P Systems with Evolutional Symport/Antiport Rules

Complexity ◽

10.1155/2018/3745210 ◽

2018 ◽

Vol 2018 ◽

pp. 1-21 ◽

Cited By ~ 10

Author(s):

Linqiang Pan ◽

Bosheng Song ◽

Luis Valencia-Cabrera ◽

Mario J. Pérez-Jiménez

Keyword(s):

Computational Complexity ◽

Natural Number ◽

Polynomial Time ◽

Cell Separation ◽

Computational Models ◽

P Systems ◽

Fission Process ◽

Work Cell ◽

Membrane Fission ◽

Biochemical Systems

Tissue P systems with evolutional communication (symport/antiport) rules are computational models inspired by biochemical systems consisting of multiple individuals living and cooperating in a certain environment, where objects can be modified when moving from one region to another region. In this work, cell separation, inspired from membrane fission process, is introduced in the framework of tissue P systems with evolutional communication rules. The computational complexity of this kind of P systems is investigated. It is proved that only problems in class P can be efficiently solved by tissue P systems with cell separation with evolutional communication rules of length at most (n,1), for each natural number n≥1. In the case where that length is upper bounded by (3,2), a polynomial time solution to the SAT problem is provided, hence, assuming that P≠NP a new boundary between tractability and NP-hardness on the basis of the length of evolutional communication rules is provided. Finally, a new simulator for tissue P systems with evolutional communication rules is designed and is used to check the correctness of the solution to the SAT problem.

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The computational power of timed P systems with active membranes using promoters

Mathematical Structures in Computer Science ◽

10.1017/s0960129518000282 ◽

2018 ◽

Vol 29 (5) ◽

pp. 663-680 ◽

Cited By ~ 2

Author(s):

YUEGUO LUO ◽

HAIJUN TAN ◽

YING ZHANG ◽

YUN JIANG

Keyword(s):

P Systems ◽

P System ◽

Computational Power ◽

Computable Set ◽

Complete Problem ◽

Active Membranes ◽

New Variant ◽

Uniform Solution ◽

Bioinspired Computing ◽

Computing Models

P systems with active membranes are a class of bioinspired computing models, where the rules are used in the non-deterministic maximally parallel manner. In this paper, first, a new variant of timed P systems with active membranes is proposed, where the application of rules can be regulated by promoters with only two polarizations. Next, we prove that any Turing computable set of numbers can be generated by such a P system in the time-free way. Moreover, we construct a uniform solution to the$\mathcal{SAT}$problem in the framework of such recognizer timed P systems in polynomial time, and the feasibility and effectiveness of the proposed system is demonstrated by an instance. Compared with the existing methods, the P systems constructed in our work require fewer necessary resources and RS-steps, which show that the solution is effective toNP-complete problem.

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On Distributed Solution to SAT by Membrane Computing

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2018.3.3217 ◽

2018 ◽

Vol 13 (3) ◽

pp. 303-320 ◽

Cited By ~ 2

Author(s):

Henry N. Adorna ◽

Linqiang Pan ◽

Bosheng Song

Keyword(s):

Cell Division ◽

Computational Models ◽

P Systems ◽

Boolean Formula ◽

Sat Problem ◽

Complete Problems ◽

Uniform Solution ◽

Boolean Formulas ◽

The Given ◽

Communication Resource

Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called $k$-distributed tissue P systems with evolutional communication and cell division ($k\text{-}\Delta_{TP_{ec}}$, for short) is proposed. A uniform solution to the SAT problem by $k\text{-}\Delta_{TP_{ec}}$ under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform $k$-P protocols are increased with respect to $k$; while a single communication is shown to be possible for bi-directional uniform $k$-P protocols for any $k$. We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem work no much faster than TPec.

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