An efficient time-free solution to SAT problem by P systems with proteins on membranes

In this paper we define a general class of P systems covering some biological operations with membranes, including evolution, communication, and modifying the membrane structure, and we describe and formally specify some of these operations: membrane merging, membrane separation, membrane release. We also investigate a particular combination of types of rules that can be used in solving the SAT problem in linear time.

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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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Evaluating the SAT problem on P systems for different high-performance architectures

The Journal of Supercomputing ◽

10.1007/s11227-014-1150-9 ◽

2014 ◽

Vol 69 (1) ◽

pp. 248-272

Author(s):

José M. Cecilia ◽

José M. García ◽

Ginés D. Guerrero ◽

Manuel Ujaldón

Keyword(s):

High Performance ◽

P Systems ◽

Sat Problem

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Time-Free Solution to Hamilton Path Problems Using P Systems withd-Division

Journal of Applied Mathematics ◽

10.1155/2013/975798 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 9

Author(s):

Tao Song ◽

Xun Wang ◽

Hongjiang Zheng

Keyword(s):

Execution Time ◽

Linear Time ◽

Hamiltonian Path ◽

P Systems ◽

Free Solution ◽

Hamilton Path ◽

Working Space ◽

A Cell ◽

Hard Problems ◽

Computing Models

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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P SYSTEMS WITH INPUT IN BINARY FORM

International Journal of Foundations of Computer Science ◽

10.1142/s0129054106003735 ◽

2006 ◽

Vol 17 (01) ◽

pp. 127-146 ◽

Cited By ~ 14

Author(s):

ALBERTO LEPORATI ◽

CLAUDIO ZANDRON ◽

MIGUEL A. GUTIÉRREZ-NARANJO

Keyword(s):

Complexity Theory ◽

Binary Form ◽

P Systems ◽

Turing Machines ◽

Simple Method ◽

Sat Problem ◽

Numerical Problem ◽

Complete Problems ◽

Np Complete

Current P systems which solve NP–complete numerical problems represent the instances of the problems in unary notation. However, in classical complexity theory, based upon Turing machines, switching from binary to unary encoded instances generally corresponds to simplify the problem. In this paper we show that, when working with P systems, we can assume without loss of generality that instances are expressed in binary notation. More precisely, we propose a simple method to encode binary numbers using multisets, and a family of P systems which transforms such multisets into the usual unary notation. Such a family could thus be composed with the unary P systems currently proposed in the literature to obtain (uniform) families of P systems which solve NP–complete numerical problems with instances encoded in binary notation. We introduce also a framework which can be used to design uniform families of P systems which solve NP–complete problems (both numerical and non-numerical) working directly on binary encoded instances, i.e., without first transforming them to unary notation. We illustrate our framework by designing a family of P systems which solves the 3-SAT problem. Next, we discuss the modifications needed to obtain a family of P systems which solves the PARTITION numerical problem.

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