The P versus NP Problem from the Membrane Computing View

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.

Download Full-text

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

Complexity ◽

10.1155/2021/7120840 ◽

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.

Download Full-text

Membrane Computing

Molecular Computational Models - Advances in Web Services Research ◽

10.4018/978-1-59140-333-3.ch001 ◽

2011 ◽

pp. 1-31 ◽

Cited By ~ 2

Author(s):

Gheorghe Paun

Keyword(s):

Membrane Computing ◽

Living Cells ◽

Point Of View ◽

Natural Computing ◽

Historical Evolution ◽

Biological Phenomena ◽

Complete Problems ◽

Hard Problems ◽

Np Complete ◽

And Mathematics

Membrane computing is a branch of natural computing whose initial goal was to abstract computing models from the structure and the functioning of living cells. The research was initiated about five years ago (at the end of 1998), and since that time the area has been developed significantly from a mathematical point of view. The basic types of results of this research concern the computability power (in comparison with the standard Turing machines and their restrictions) and the efficiency (the possibility to solve computationally hard problems, typically NP-complete problems, in a feasible time and typically polynomial). However, membrane computing has recently become attractive also as a framework for devising models of biological phenomena, with the tendency to provide tools for modelling the cell itself, not only the local processes. This chapter surveys the basic elements of membrane computing, somewhat in its “historical” evolution: from biology to computer science and mathematics and back to biology. The presentation is informal, without any technical detail, and an invitation to membrane computing intended to acquaint the nonmathematician reader with the main directions of research of the domain, the type of central results, and the possible lines of future development, including the possible interest of the biologist looking for discrete algorithmic tools for modelling cell phenomena.

Download Full-text

Software for Membrane Computing

Robotic Systems ◽

10.4018/978-1-7998-1754-3.ch035 ◽

2020 ◽

pp. 659-678

Author(s):

Andrei George Florea ◽

Cătălin Buiu

Keyword(s):

Real World ◽

Membrane Computing ◽

Real Life ◽

Natural Computing ◽

Software Application ◽

The World ◽

Definition Of ◽

And Robotics ◽

Computing Models ◽

Detailed Presentation

In order to use membrane computing models for real life applications there is a real need for software that can read a model from some form of input media and afterwards execute it according to the execution rules that are specified in the definition of the model. Another requirement of this software application is for it to be capable of interfacing the computing model with the real world. This chapter discusses how this problem was solved along the years by various researchers around the world. After presenting notable examples from the literature, the discussion continues with a detailed presentation of three membrane computing simulators that have been developed by the authors at the Laboratory of Natural Computing and Robotics at the Politehnica University of Bucharest, Romania.

Download Full-text

Membrane Computing Model Design with Quantum-Inspired Evolutionary Algorithms

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.655-657.1761 ◽

2013 ◽

Vol 655-657 ◽

pp. 1761-1764 ◽

Cited By ~ 2

Author(s):

Hai Na Rong ◽

Xiao Li Huang

Keyword(s):

Membrane Computing ◽

Design Method ◽

Main Idea ◽

Natural Computing ◽

Automatic Design ◽

Model Design ◽

Evolution Rule ◽

Computing Model ◽

Rule Set ◽

Computing Models

As a branch of natural computing, membrane computing has attracted much attention in various disciplines. But the programmability of membrane computing models is an ongoing and challenging issue in this area. This paper develops the automatic design of membrane computing models through predefining the membrane structure and initial objects and introducing a modified quantum-inspired evolutionary algorithm with a local disturbance to select an appropriate subset from a redundant evolution rule set. The main idea of the presented method is that multiple membrane computing models, instead of only one model like in the literature, can be designed by applying one redundant evolution rule set. The effectiveness of the design method is verified by the experiments.

Download Full-text

Simple Neural-Like P Systems for Maximal Independent Set Selection

Neural Computation ◽

10.1162/neco_a_00443 ◽

2013 ◽

Vol 25 (6) ◽

pp. 1642-1659 ◽

Cited By ~ 7

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.

Download Full-text

Solution to PSPACE-Complete Problem Using P Systems with Active Membranes with Time-Freeness

Mathematical Problems in Engineering ◽

10.1155/2019/5793234 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 14

Author(s):

Bosheng Song ◽

Yuan Kong

Keyword(s):

Execution Time ◽

Cell Structure ◽

P Systems ◽

Biological Information ◽

Natural Computing ◽

Boolean Satisfiability Problem ◽

Active Membranes ◽

Hard Problems ◽

And Behavior ◽

Computing Models

P systems with active membranes are powerful parallel natural computing models, which were inspired by cell structure and behavior. Inspired by the parallel processing of biological information and with the idealistic assumption that each rule is completed in exactly one time unit, P systems with active membranes are able to solve computational hard problems in a feasible time. However, an important biological fact in living cells is that the execution time of a biochemical reaction cannot be accurately divided equally and completed in one time unit. In this work, we consider time as an important factor for the computation in P systems with active membranes and investigate the computational efficiency of such P systems. Specifically, we present a time-free semiuniform solution to the quantified Boolean satisfiability problem (QSATproblem, for short) in the framework of P systems with active membranes, where the solution to such problem is correct, which does not depend on the execution time for the used rules.

Download Full-text

Time-free Solution to Independent Set Problem using P Systems with Active Membranes

Fundamenta Informaticae ◽

10.3233/fi-2021-2072 ◽

2021 ◽

Vol 182 (3) ◽

pp. 243-255

Author(s):

Yu Jin ◽

Bosheng Song ◽

Yanyan Li ◽

Ying Zhu

Keyword(s):

Membrane Computing ◽

Independent Set ◽

P Systems ◽

Natural Computing ◽

Free Solution ◽

Independent Set Problem ◽

Global Clock ◽

Active Membranes ◽

Biological Reality ◽

Hard Problems

Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problem using P systems with active membranes, which solve the problem independent of the execution time of the involved rules.

Download Full-text

Software for Membrane Computing

Advances in Computational Intelligence and Robotics - Membrane Computing for Distributed Control of Robotic Swarms ◽

10.4018/978-1-5225-2280-5.ch003 ◽

2017 ◽

pp. 35-58

Keyword(s):

Real World ◽

Membrane Computing ◽

Real Life ◽

Natural Computing ◽

Software Application ◽

The World ◽

Definition Of ◽

And Robotics ◽

Computing Models ◽

Detailed Presentation

Download Full-text

From NP-Completeness to DP-Completeness: A Membrane Computing Perspective

Complexity ◽

10.1155/2020/6765097 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

Luis Valencia-Cabrera ◽

David Orellana-Martín ◽

Miguel Á. Martínez-del-Amor ◽

Ignacio Pérez-Hurtado ◽

Mario J. Pérez-Jiménez

Keyword(s):

Lower Bound ◽

Polynomial Time ◽

Time Complexity ◽

Membrane Computing ◽

Decision Problems ◽

Membrane Systems ◽

Np Completeness ◽

Computing Model ◽

Complete Problems ◽

Computing Models

Presumably efficient computing models are characterized by their capability to provide polynomial-time solutions for NP-complete problems. Given a class ℛ of recognizer membrane systems, ℛ denotes the set of decision problems solvable by families from ℛ in polynomial time and in a uniform way. PMCℛ is closed under complement and under polynomial-time reduction. Therefore, if ℛ is a presumably efficient computing model of recognizer membrane systems, then NP ∪ co-NP ⊆ PMCℛ. In this paper, the lower bound NP ∪ co-NP for the time complexity class PMCℛ is improved for any presumably efficient computing model ℛ of recognizer membrane systems verifying some simple requirements. Specifically, it is shown that DP ∪ co-DP is a lower bound for such PMCℛ, where DP is the class of differences of any two languages in NP. Since NP ∪ co-NP ⊆ DP ∩ co-DP, this lower bound for PMCℛ delimits a thinner frontier than that with NP ∪ co-NP.

Download Full-text

On the Concepts of Parallelism in Biomolecular Computing

Triangle ◽

10.17345/triangle6.109-118 ◽

2018 ◽

pp. 109

Author(s):

Remco Loos ◽

Bendek Nagy

Keyword(s):

Problem Solving ◽

Membrane Computing ◽

Theoretical Models ◽

Natural Computing ◽

Biomolecular Computing ◽

Hard Problems

In this paper we consider DNA and membrane computing, both as theoretical models and as problem solving devices. The basic motivation behind these models of natural computing is using parallelism to make hard problems tractable. In this paper we analyze the concept of parallelism. We will show that parallelism has very different meanings in these models.We introduce the terms ’or-parallelism’ and ’and-parallelism’ for these two basic types of parallelism.

Download Full-text