Simple Neural-Like P Systems for Maximal Independent Set Selection

2013 ◽  
Vol 25 (6) ◽  
pp. 1642-1659 ◽  
Author(s):  
Lei Xu ◽  
Peter Jeavons
Keyword(s):  
Distributed Computing ◽  
Membrane Computing ◽  
Independent Set ◽  
Living Cells ◽  
P Systems ◽  
Maximal Independent Set ◽  
Membrane Systems ◽  
New Class ◽  
The Individual ◽  
Computing Models

Membrane systems (P systems) are distributed computing models inspired by living cells where a collection of processors jointly achieves a computing task. The problem of maximal independent set (MIS) selection in a graph is to choose a set of nonadjacent nodes to which no further nodes can be added. In this letter, we design a class of simple neural-like P systems to solve the MIS selection problem efficiently in a distributed way. This new class of systems possesses two features that are attractive for both distributed computing and membrane computing: first, the individual processors do not need any information about the overall size of the graph; second, they communicate using only one-bit messages.

scholarly journals Generation of Two-Dimensional Grammar Based Pattern Languages using Array Rewriting P System

2019 ◽  
Vol 8 (12) ◽  
pp. 1271-1276
Keyword(s):  
Theoretical Model ◽  
Computational Model ◽  
Special Interest ◽  
Membrane Computing ◽  
Living Cells ◽  
P Systems ◽  
P System ◽  
Two Dimensional ◽  
Pattern Languages ◽  
New Class

The theory of membrane computing was formulated by Paun as an attempt to formulate a computational model inspired by the way in which the living cells function. P systems which is a highly distributed, parallel, theoretical model and is an area of special interest in recent times. P systems have various application one such area of research is the generation of array grammars using them. In this study we define a model of P system to generate a new class of languages called grammar based two-dimensional pattern languages and their picture generation.

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.

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.

Membrane Computing

2017 ◽  
pp. 15-34
Keyword(s):  
Robot Control ◽  
Membrane Computing ◽  
P Systems ◽  
System Model ◽  
P System ◽  
Input Output ◽  
Control Models ◽  
P Colonies ◽  
Theoretical Computing ◽  
Computing Models

The theoretical computing models that are used throughout this book are described in this chapter. These models are based on the initial P system model and include: Numerical P systems, Enzymatic Numerical P systems, P colonies and P swarms. Detailed examples and execution diagrams help the reader allow the reader to understand the functioning principle of each model and also its potential in various applications. The similarity between P systems (and their variants) and robot control models is also addressed. This analysis is presented to the reader in a side-by-side manner using a table where each row represents an analysis topic. Among others we mention: (1) Architectural structure, (2) Modularity and hierarchy, (3) Input-output relationships, (4) Parallelism.

scholarly journals Simulation of Rapidly-Exploring Random Trees in Membrane Computing with P-Lingua and Automatic Programming

2018 ◽  
Vol 13 (6) ◽  
pp. 1007-1031 ◽  
Author(s):  
Ignacio Perez-Hurtado ◽  
Mario Perez-Jumenez ◽  
Gexiang Zhang ◽  
David Orellana-Martin
Keyword(s):  
Membrane Computing ◽  
Ad Hoc ◽  
Multicore Processors ◽  
Random Trees ◽  
P Systems ◽  
Automatic Programming ◽  
C Language ◽  
Rapidly Exploring Random Trees ◽  
Planning Problems ◽  
Computing Models

Methods based on Rapidly-exploring Random Trees (RRTs) have been widely used in robotics to solve motion planning problems. On the other hand, in the membrane computing framework, models based on Enzymatic Numerical P systems (ENPS) have been applied to robot controllers, but today there is a lack of planning algorithms based on membrane computing for robotics. With this motivation, we provide a variant of ENPS called Random Enzymatic Numerical P systems with Proteins and Shared Memory (RENPSM) addressed to implement RRT algorithms and we illustrate it by simulating the bidirectional RRT algorithm. This paper is an extension of [21]a. The software presented in [21] was an ad-hoc simulator, i.e, a tool for simulating computations of one and only one model that has been hard-coded. The main contribution of this paper with respect to [21] is the introduction of a novel solution for membrane computing simulators based on automatic programming. First, we have extended the P-Lingua syntax –a language to define membrane computing models– to write RENPSM models. Second, we have implemented a new parser based on Flex and Bison to read RENPSM models and produce source code in C language for multicore processors with OpenMP. Finally, additional experiments are presented.

FURTHER RESULTS ON TIME-FREE P SYSTEMS

2006 ◽  
Vol 17 (01) ◽  
pp. 69-89 ◽  
Author(s):  
MATTEO CAVALIERE ◽  
VINCENZO DEUFEMIA
Keyword(s):  
Parallel Computing ◽  
Chemical Reactions ◽  
Living Cells ◽  
P Systems ◽  
P System ◽  
Membrane Systems ◽  
Open Problems ◽  
Free Evolution ◽  
Cooperative Evolution ◽  
Weight One

Membrane systems (currently called P systems) are parallel computing devices inspired by the structure and the functioning of living cells. A standard feature of P systems is that each rule is executed in exactly one time unit. Actually, in living cells different chemical reactions might take different times to be executed; moreover, it might be hard to know precisely such time of execution. For this reason, in [7] two models of P systems (time-free and clock-free P systems) have been defined and investigated, where the time of execution of the rules is arbitrary and the output produced by the system is always the same, independently of this time. Preliminary results concerning time-free and clock-free P system have been obtained in [6, 7, 8]. In this paper we continue these investigations by considering different combinations of possible ingredients. In particular, we present the universality of time-free P systems using bi-stable catalysts. Then, we prove that this result implies that is not possible to decide whether an arbitrary bi-stable catalytic P system is time-free. We present several results about time-free evolution-communication P systems, where the computation is a mixed application of evolution and symport/antiport rules. In this case we obtain the universality even by using non-cooperative evolution rules and antiports of weight one. Finally, we formulate several open problems.

The P versus NP Problem from the Membrane Computing View

2014 ◽  
Vol 22 (1) ◽  
pp. 18-33 ◽  
Author(s):  
Mario J. Pérez-Jiménez
Keyword(s):  
Membrane Computing ◽  
Efficient Solutions ◽  
Significant Advance ◽  
Natural Computing ◽  
Complexity Classes ◽  
Membrane Systems ◽  
Hard Problems ◽  
Young Branch ◽  
Np Problem ◽  
Computing Models

In the last few decades several computing models using powerful tools from Nature have been developed (because of this, they are known as bio-inspired models). Commonly, the space-time trade-off method is used to develop efficient solutions to computationally hard problems. According to this, implementation of such models (in biological, electronic, or any other substrate) would provide a significant advance in the practical resolution of hard problems. Membrane Computing is a young branch of Natural Computing initiated by Gh. Păun at the end of 1998. It is inspired by the structure and functioning of living cells, as well as from the organization of cells in tissues, organs, and other higher order structures. The devices of this paradigm, called P systems or membrane systems, constitute models for distributed, parallel and non-deterministic computing. In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented. Different borderlines between efficiency and non-efficiency are shown, and many attractive characterizations of the P ≠ NP conjecture within the framework of this bio-inspired and non-conventional computing model are studied.

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.

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