A Linear-Time Solution to the Knapsack Problem Using P Systems with Active 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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Solving SAT by P Systems with Active Membranes in Linear Time in the Number of Variables

Membrane Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-642-54239-8_14 ◽

2014 ◽

pp. 189-205 ◽

Cited By ~ 4

Author(s):

Zsolt Gazdag

Keyword(s):

Linear Time ◽

P Systems ◽

Active Membranes

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Semi-Uniform Solution for Common Algorithmic Problem by P System in the Minimally Parallel Mode

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.568-570.802 ◽

2014 ◽

Vol 568-570 ◽

pp. 802-806

Author(s):

Yun Yun Niu ◽

Zhi Gao Wang

Keyword(s):

Linear Time ◽

P Systems ◽

P System ◽

Algorithmic Problem ◽

Complete Problems ◽

Active Membranes ◽

Uniform Solution ◽

Parallel Mode ◽

The Common ◽

Np Complete

It is known that the Common Algorithmic Problem (CAP) has a nice property that several other NP-complete problems can be reduced to it in linear time. In the literature, the decision version of this problem can be efficiently solved with a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes that do not use polarizations and present a semi-uniform solution to CAP in the minimally parallel mode.

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Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division

International Journal of Natural Computing Research ◽

10.4018/jncr.2011070105 ◽

2011 ◽

Vol 2 (3) ◽

pp. 49-60 ◽

Cited By ~ 1

Author(s):

Xingyi Zhang ◽

Yunyun Niu ◽

Linqiang Pan ◽

Mario J. Pérez-Jiménez

Keyword(s):

Cell Division ◽

Quantum Computer ◽

Linear Time ◽

Public Key Cryptography ◽

Polynomial Time Algorithm ◽

P Systems ◽

Public Key ◽

Prime Factorization ◽

Factorization Problem ◽

Time Solution

Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer was given by P. W. Shor in 1997. In this work, it is considered as a function problem, and in the framework of tissue P systems with cell division, a linear-time solution to prime factorization problem is given on biochemical computational devices – tissue P systems with cell division, instead of computational devices based on the laws of quantum physical.

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Linear Time Solution to Prime Factorization by Tissue P Systems with Cell Division

Natural Computing for Simulation and Knowledge Discovery ◽

10.4018/978-1-4666-4253-9.ch014 ◽

2014 ◽

pp. 207-220

Author(s):

Xingyi Zhang ◽

Yunyun Niu ◽

Linqiang Pan ◽

Mario J. Pérez-Jiménez

Keyword(s):

Cell Division ◽

Quantum Computer ◽

Linear Time ◽

Public Key Cryptography ◽

Polynomial Time Algorithm ◽

P Systems ◽

Public Key ◽

Prime Factorization ◽

Factorization Problem ◽

Time Solution

Prime factorization is useful and crucial for public-key cryptography, and its application in public-key cryptography is possible only because prime factorization has been presumed to be difficult. A polynomial-time algorithm for prime factorization on a quantum computer was given by P. W. Shor in 1997. In this work, it is considered as a function problem, and in the framework of tissue P systems with cell division, a linear-time solution to prime factorization problem is given on biochemical computational devices – tissue P systems with cell division, instead of computational devices based on the laws of quantum physical.

Download Full-text