scholarly journals P Systems with Evolutional Communication and Division Rules

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 327
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Membrane Computing ◽  
P Systems ◽  
Membrane Systems ◽  
Sat Problem ◽  
Complete Problem ◽  
Intractable Problems ◽  
Np Complete ◽  
The One

A widely studied field in the framework of membrane computing is computational complexity theory. While some types of P systems are only capable of efficiently solving problems from the class P, adding one or more syntactic or semantic ingredients to these membrane systems can give them the ability to efficiently solve presumably intractable problems. These ingredients are called to form a frontier of efficiency, in the sense that passing from the first type of P systems to the second type leads to passing from non-efficiency to the presumed efficiency. In this work, a solution to the SAT problem, a well-known NP-complete problem, is obtained by means of a family of recognizer P systems with evolutional symport/antiport rules of length at most (2,1) and division rules where the environment plays a passive role; that is, P systems from CDEC^(2,1). This result is comparable to the one obtained in the tissue-like counterpart, and gives a glance of a parallelism and the non-evolutionary membrane systems with symport/antiport rules.

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 When catalytic P systems with one catalyst can be computationally complete

2021 ◽  
Author(s):  
Artiom Alhazov ◽  
Rudolf Freund ◽  
Sergiu Ivanov
Keyword(s):  
Computational Complexity ◽  
P Systems ◽  
Membrane Systems ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
Recursively Enumerable Sets

AbstractCatalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.

scholarly journals Impact of Membrane Computing and P Systems in ISI WoS. Celebrating the 65th Birthday of Gheorghe Păun

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ioan DZITAC
Keyword(s):  
Computer Science ◽  
Membrane Computing ◽  
Research Area ◽  
P Systems ◽  
65Th Birthday ◽  
Membrane Systems ◽  
Journal Paper ◽  
Technical Report ◽  
The Impact

Membrane Computing is a branch of Computer Science initiated by<br />Gheorghe Păun in 1998, in a technical report of Turku Centre for Computer Science<br />published as a journal paper ("Computing with Membranes" in Journal of Computer<br />and System Sciences) in 2000. Membrane systems, as Gheorghe Păun called the<br />models he has introduced, are known nowadays as "P Systems" (with the letter P<br />coming from the initial of the name of this research area "father").<br />This note is an overview of the impact in ISI WoS of Gheorghe Păun’s works, focused<br />on Membrane Computing and P Systems field, on the occasion of his 65th birthday<br />anniversary.

COMPUTING WITH MEMBRANES (P SYSTEMS): A VARIANT

2000 ◽  
Vol 11 (01) ◽  
pp. 167-181 ◽  
Author(s):  
GHEORGHE PĂUN
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Pass Through ◽  
The One ◽  
Priority Relation ◽  
Recursively Enumerable Languages ◽  
Biochemical Features ◽  
Computing Models

Membrane Computing is a recently introduced area of Molecular Computing, where a computation takes place in a membrane structure where multisets of objects evolve according to given rules (they can also pass through membranes). The obtained computing models were called P systems. In basic variants of P systems, the use of objects evolution rules is regulated by a given priority relation; moreover, each membrane has a label and one can send objects to precise membranes, identified by their labels. We propose here a variant where we get rid of both there rather artificial (non-biochemical) features. Instead, we add to membranes and to objects an "electrical charge" and the objects are passed through membranes according to their charge. We prove that such systems are able to characterize the one-letter recursively enumerable languages (equivalently, the recursively enumerable sets of natural numbers), providing that an extra feature is considered: the membranes can be made thicker or thinner (also dissolved) and the communication through a membrane is possible only when its thickness is equal to 1. Several open problems are formulated.

A Note on the Ohya-Masuda Quantum Algorithm

2002 ◽  
Vol 09 (02) ◽  
pp. 115-123
Author(s):  
Miroljub Dugić
Keyword(s):  
Density Matrix ◽  
Complexity Theory ◽  
Quantum Measurement ◽  
Pure State ◽  
Quantum Algorithm ◽  
Satisfiability Problem ◽  
Second Step ◽  
Coherent Superposition ◽  
Complete Problem ◽  
Np Complete

We analyze the Ohya-Masuda quantum algorithm that solves the so-called “satisfiability” problem, which is an NP-complete problem of the complexity theory. We distinguish three steps in the algorithm, and analyze the second step, in which a coherent superposition of states (a “pure” state) transforms into an “incoherent” mixture presented by a density matrix. We show that, if “nonideal” (in analogy with “nonideal” quantum measurement), this transformation can make the algorithm to fail in some cases. On this basis we give some general notions on the physical implementation of the Ohya-Masuda algorithm.

An Efficient Technique to Ensure the Logical Consistency of Interacting Knowledge Bases

1997 ◽  
Vol 06 (01) ◽  
pp. 27-36 ◽  
Author(s):  
Bertrand Mazure ◽  
Lakhdar Saïs ◽  
Éric Grégoire
Keyword(s):  
Local Search ◽  
Fundamental Problem ◽  
Real Life ◽  
Knowledge Bases ◽  
The Other ◽  
Logical Consistency ◽  
Complete Problem ◽  
Np Complete ◽  
The One ◽  
Cooperative Knowledge

In this paper, we address a fundamental problem in the formalization and implementation of cooperative knowledge bases: the difficulty of preserving consistency while interacting or combining them. Indeed, knowledge bases that are individually consistent can exhibit global inconsistency. This stumbling-block problem is an even more serious drawback when knowledge and reasoning are expressed using logical terms. Indeed, on the one hand, two contradictory pieces of information lead to global inconsistency under complete standard rules of deduction: every assertion and its contrary can be deduced. On the other hand, checking the logical consistency of a propositional knowledge base is an NP-complete problem and is often out of reach for large real-life applications. In this paper, a new practical technique to locate inconsistent interacting pieces of information is presented in the context of cooperative logical knowledge bases. Based on a recently discovered heuristic about the work performed by local search techniques, it can be applied in the context of large interacting knowledge bases.

scholarly journals Dictionary Search and Update by P Systems with String-Objects and Active Membranes

2009 ◽  
Vol 4 (3) ◽  
pp. 206
Author(s):  
Artiom Alhazov ◽  
Svetlana Cojocaru ◽  
Ludmila Malahova ◽  
Yurii Rogozhin
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Membrane Systems ◽  
Prefix Tree ◽  
Active Membranes ◽  
Formal Framework

Membrane computing is a formal framework of distributed parallel com- puting. In this paper we implement the work with the prefix tree by P systems with strings and active membranes. We present the algorithms of searching in a dictionary and updating it implemented as membrane systems. The systems are constructed as reusable modules, so they are suitable for using as sub-algorithms for solving more complicated problems.

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.

Spiking Neural P Systems

2011 ◽  
pp. 60-73 ◽  
Author(s):  
Gheorghe Paun ◽  
Mario J. Perez-Jimenez
Keyword(s):  
Computational Complexity ◽  
Membrane Computing ◽  
Research Area ◽  
P Systems ◽  
Neural Computing ◽  
Research Topics ◽  
Computing Power ◽  
Spiking Neural P Systems ◽  
Basic Ideas ◽  
Source Of Information

This chapter is a quick survey of spiking neural P systems, a branch of membrane computing which was recently introduced with motivation from neural computing based on spiking. Basic ideas, examples, some results (especially concerning the computing power and the computational complexity/efficiency), and several research topics are discussed. The presentation is succinct and informal, meant mainly to let the reader having a flavour of this research area. The additional references are an important source of information in this respect.

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