Solving NP-Complete Problems Using P Systems with Active Membranes

2001 ◽  
pp. 289-301 ◽  
Author(s):  
Claudio Zandron ◽  
Claudio Ferretti ◽  
Giancarlo Mauri
Keyword(s):  
P Systems ◽  
Complete Problems ◽  
Active Membranes ◽  
Np Complete

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

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.

scholarly journals On the power of P systems with active membranes using weak non-elementary membrane division

2021 ◽  
Author(s):  
Zsolt Gazdag ◽  
Károly Hajagos ◽  
Szabolcs Iván
Keyword(s):  
Polynomial Time ◽  
P Systems ◽  
Computational Power ◽  
Complete Problems ◽  
Active Membranes ◽  
Membrane Division ◽  
Elementary Membrane

AbstractIt is known that polarizationless P systems with active membranes can solve $$\mathrm {PSPACE}$$ PSPACE -complete problems in polynomial time without using in-communication rules but using the classical (also called strong) non-elementary membrane division rules. In this paper, we show that this holds also when in-communication rules are allowed but strong non-elementary division rules are replaced with weak non-elementary division rules, a type of rule which is an extension of elementary membrane divisions to non-elementary membranes. Since it is known that without in-communication rules, these P systems can solve in polynomial time only problems in $$\mathrm {P}^{\text {NP}}$$ P NP , our result proves that these rules serve as a borderline between $$\mathrm {P}^{\text {NP}}$$ P NP and $$\mathrm {PSPACE}$$ PSPACE concerning the computational power of these P systems.

scholarly journals Tuning Frontiers of Efficiency in Tissue P Systems with Evolutional Communication Rules

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Bosheng Song ◽  
Linqiang Pan ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Polynomial Time ◽  
Efficient Solution ◽  
Efficient Solutions ◽  
Affirmative Answer ◽  
P Systems ◽  
Membrane Systems ◽  
Complete Problems ◽  
Np Complete ◽  
Np Problem ◽  
Computing Models

Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

scholarly journals A new method to simulate restricted variants of polarizationless P systems with active membranes

2019 ◽  
Vol 1 (4) ◽  
pp. 251-261 ◽  
Author(s):  
Zsolt Gazdag ◽  
Gábor Kolonits
Keyword(s):  
Membrane Structure ◽  
P Systems ◽  
New Approach ◽  
Complete Problems ◽  
Active Membranes ◽  
Special Cases ◽  
Division Polynomials ◽  
Initial Membrane ◽  
Membrane Division ◽  
Elementary Membrane

AbstractAccording to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve $${\mathbf {NP}}$$NP-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes

2009 ◽  
pp. 108-117 ◽  
Author(s):  
Artiom Alhazov ◽  
Liudmila Burtseva ◽  
Svetlana Cojocaru ◽  
Yurii Rogozhin
Keyword(s):  
P Systems ◽  
Complete Problems ◽  
Active Membranes

The power of time-free tissue P systems: Attacking NP-complete problems

2015 ◽  
Vol 159 ◽  
pp. 151-156 ◽  
Author(s):  
Xiangrong Liu ◽  
Juan Suo ◽  
Stephen C.H. Leung ◽  
Juan Liu ◽  
Xiangxiang Zeng
Keyword(s):  
P Systems ◽  
Complete Problems ◽  
Np Complete

scholarly journals Solving Vertex Cover Problem by Means of Tissue P Systems with Cell Separation

2010 ◽  
Vol 5 (4) ◽  
pp. 540 ◽  
Author(s):  
Chun Lu ◽  
Xingyi Zhang
Keyword(s):  
Cell Separation ◽  
Membrane Computing ◽  
Linear Time ◽  
Vertex Cover ◽  
P Systems ◽  
Computing Model ◽  
Vertex Cover Problem ◽  
Complete Problems ◽  
Np Complete ◽  
Cover Problem

Tissue P systems is a computing model in the framework of membrane computing inspired from intercellular communication and cooperation between neurons. Many different variants of this model have been proposed. One of the most important models is known as tissue P systems with cell separation. This model has the ability of generating an exponential amount of workspace in linear time, thus it allows us to design cellular solutions to NP-complete problems in polynomial time. In this paper, we present a solution to the Vertex Cover problem via a family of such devices. This is the first solution to this problem in the framework of tissue P systems with cell separation.

Cellular Solutions to Some Numerical NP-Complete Problems

2011 ◽  
pp. 115-149 ◽  
Author(s):  
Andrés Cordón-Franco ◽  
Miguel A. Gutiérrez-Naranjo ◽  
Mario J. Pérez-Jiménez ◽  
Agustín Riscos-Núñez
Keyword(s):  
Polynomial Time ◽  
Efficient Solutions ◽  
Cellular Systems ◽  
P Systems ◽  
Knapsack Problems ◽  
Simulation Tool ◽  
Working Space ◽  
Complete Problems ◽  
Subset Sum ◽  
Np Complete

This chapter is devoted to the study of numerical NP-complete problems in the framework of cellular systems with membranes, also called P systems (Pun, 1998). The chapter presents efficient solutions to the subset sum and the knapsack problems. These solutions are obtained via families of P systems with the capability of generating an exponential working space in polynomial time. A simulation tool for P systems, written in Prolog, is also described. As an illustration of the use of this tool, the chapter includes a session in the Prolog simulator implementing an algorithm to solve one of the above problems.

P SYSTEMS WITH INPUT IN BINARY FORM

2006 ◽  
Vol 17 (01) ◽  
pp. 127-146 ◽  
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.

scholarly journals Solving NP-Complete Problems by Spiking Neural P Systems with Budding Rules

2010 ◽  
pp. 335-353 ◽  
Author(s):  
Tseren-Onolt Ishdorj ◽  
Alberto Leporati ◽  
Linqiang Pan ◽  
Jun Wang
Keyword(s):  
P Systems ◽  
Spiking Neural P Systems ◽  
Complete Problems ◽  
Np Complete
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