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

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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
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.

scholarly journals COMPUTATION OF RAMSEY NUMBERS BY P SYSTEMS WITH ACTIVE MEMBRANES

2011 ◽  
Vol 22 (01) ◽  
pp. 29-38 ◽  
Author(s):  
LINQIANG PAN ◽  
DANIEL DÍAZ-PERNIL ◽  
MARIO J. PÉREZ-JIMÉNEZ
Keyword(s):  
Membrane Computing ◽  
P Systems ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Combinatorial Object ◽  
Active Membranes ◽  
Number Problem ◽  
Decision Version

Ramsey numbers deal with conditions when a combinatorial object necessarily contains some smaller given objects. It is well known that it is very difficult to obtain the values of Ramsey numbers. In this work, a theoretical chemical/biological solution is presented in terms of membrane computing for the decision version of Ramsey number problem, that is, to decide whether an integer n is the value of Ramsey number R(k, l), where k and l are integers.

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.

Membrane Computing

2011 ◽  
pp. 1-31 ◽  
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.

scholarly journals Time-Free Solution to Hamilton Path Problems Using P Systems withd-Division

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Tao Song ◽  
Xun Wang ◽  
Hongjiang Zheng
Keyword(s):  
Execution Time ◽  
Linear Time ◽  
Hamiltonian Path ◽  
P Systems ◽  
Free Solution ◽  
Hamilton Path ◽  
Working Space ◽  
A Cell ◽  
Hard Problems ◽  
Computing Models

P systems withd-division are a particular class of distributed and parallel computing models investigated in membrane computing, which are inspired from the budding behavior of Baker’s yeast (a cell can generate several cells in one reproducing cycle). In previous works, such systems can theoretically generate exponential working space in linear time and thus provide a way to solve computational hard problems in polynomial time by a space-time tradeoff, where the precise execution time of each evolution rule, one time unit, plays a crucial role. However, the restriction that each rule has a precise same execution time does not coincide with the biological fact, since the execution time of biochemical reactions can vary because of external uncontrollable conditions. In this work, we consider timed P systems withd-division by adding a time mapping to the rules to specify the execution time for each rule, as well as the efficiency of the systems. As a result, a time-free solution to Hamiltonian path problem (HPP) is obtained by a family of such systems (constructed in a uniform way), that is, the execution time of the rules (specified by different time mappings) has no influence on the correctness of the solution.

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 Time-free solution to SAT problem using P systems with active membranes

2014 ◽  
Vol 529 ◽  
pp. 61-68 ◽  
Author(s):  
Tao Song ◽  
Luis F. Macías-Ramos ◽  
Linqiang Pan ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
P Systems ◽  
Free Solution ◽  
Sat Problem ◽  
Active Membranes

ON A PARTIAL AFFIRMATIVE ANSWER FOR A PĂUN'S CONJECTURE

2011 ◽  
Vol 22 (01) ◽  
pp. 55-64 ◽  
Author(s):  
IGNACIO PÉREZ-HURTADO ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
AGUSTÍN RISCOS-NÚÑEZ ◽  
MIGUEL A. GUTIÉRREZ-NARANJO ◽  
MIQUEL RIUS-FONT
Keyword(s):  
Affirmative Answer ◽  
Positive Answer ◽  
Dependency Graph ◽  
P Systems ◽  
Complete Proof ◽  
Active Membranes ◽  
Hard Problems

At the beginning of 2005, Gheorghe Păun formulated a conjecture stating that in the framework of recognizer P systems with active membranes (evolution rules, communication rules, dissolution rules and division rules for elementary membranes), polarizations cannot be avoided in order to solve computationally hard problems efficiently (assuming that P ≠ NP ). At the middle of 2005, a partial positive answer was given, proving that the conjecture holds if dissolution rules are forbidden. In this paper we give a detailed and complete proof of this result modifying slightly the notion of dependency graph associated with recognizer P systems.

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