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.

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.

scholarly journals Time-Free Solution to SAT Problem by Tissue P Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Yueguo Luo ◽  
Zhongyang Xiong ◽  
Guanghua Zhang
Keyword(s):  
Intercellular Communication ◽  
Execution Time ◽  
Efficient Solution ◽  
Point Of View ◽  
P Systems ◽  
Free Solution ◽  
Complete Problem ◽  
Np Complete ◽  
First Time ◽  
Computing Models

Tissue P systems are a class of computing models inspired by intercellular communication, where the rules are used in the nondeterministic maximally parallel manner. As we know, the execution time of each rule is the same in the system. However, the execution time of biochemical reactions is hard to control from a biochemical point of view. In this work, we construct a uniform and efficient solution to the SAT problem with tissue P systems in a time-free way for the first time. With the P systems constructed from the sizes of instances, the execution time of the rules has no influence on the computation results. As a result, we prove that such system is shown to be highly effective for NP-complete problem even in a time-free manner with communication rules of length at most 3.

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.

TISSUE-LIKE P SYSTEMS WITH DYNAMICALLY EMERGING REQUESTS

2008 ◽  
Vol 19 (03) ◽  
pp. 729-745 ◽  
Author(s):  
ERZSÉBET CSUHAJ-VARJÚ ◽  
GHEORGHE PĂUN ◽  
GYÖRGY VASZIL
Keyword(s):  
Polynomial Time ◽  
P Systems ◽  
Computationally Efficient ◽  
Complete Problems ◽  
Np Complete

We study tissue-like P systems which use string objects and communicate by introducing communication symbols in the strings. We prove that these systems are computationally complete and moreover, they are computationally efficient in the sense that NP-complete problems can be solved in this framework in polynomial time.

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

Complexity ◽  
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.

NONLINEAR COMPUTABILITY BASED ON CHAOS

2000 ◽  
Vol 10 (02) ◽  
pp. 415-429 ◽  
Author(s):  
GABRIELE MANGANARO ◽  
JOSE PINEDA DE GYVEZ
Keyword(s):  
Hamiltonian Path ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Information Coding ◽  
Computing Power ◽  
Complete Problems ◽  
Np Complete ◽  
Systematic Solution ◽  
Chaotic Simulated Annealing ◽  
Computing Models

Two new computing models based on information coding and chaotic dynamical systems are presented. The novelty of these models lies on the blending of chaos theory and information coding to solve complex combinatorial problems. A unique feature of our computing models is that despite the nonpredictability property of chaos, it is possible to solve any combinatorial problem in a systematic way, and with only one dynamical system. This is in sharp contrast to methods based on heuristics employing an array of chaotic cells. To prove the computing power and versatility of our models, we address the systematic solution of classical NP-complete problems such as the three colorability and the directed Hamiltonian path in addition to a new chaotic simulated annealing scheme.

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.

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