The computational power of timed P systems with active membranes using promoters

2018 ◽  
Vol 29 (5) ◽  
pp. 663-680 ◽  
Author(s):  
YUEGUO LUO ◽  
HAIJUN TAN ◽  
YING ZHANG ◽  
YUN JIANG
Keyword(s):  
P Systems ◽  
P System ◽  
Computational Power ◽  
Computable Set ◽  
Complete Problem ◽  
Active Membranes ◽  
New Variant ◽  
Uniform Solution ◽  
Bioinspired Computing ◽  
Computing Models

P systems with active membranes are a class of bioinspired computing models, where the rules are used in the non-deterministic maximally parallel manner. In this paper, first, a new variant of timed P systems with active membranes is proposed, where the application of rules can be regulated by promoters with only two polarizations. Next, we prove that any Turing computable set of numbers can be generated by such a P system in the time-free way. Moreover, we construct a uniform solution to the$\mathcal{SAT}$problem in the framework of such recognizer timed P systems in polynomial time, and the feasibility and effectiveness of the proposed system is demonstrated by an instance. Compared with the existing methods, the P systems constructed in our work require fewer necessary resources and RS-steps, which show that the solution is effective toNP-complete problem.

Semi-Uniform Solution for Common Algorithmic Problem by P System in the Minimally Parallel Mode

2014 ◽  
Vol 568-570 ◽  
pp. 802-806
Author(s):  
Yun Yun Niu ◽  
Zhi Gao Wang
Keyword(s):  
Linear Time ◽  
P Systems ◽  
P System ◽  
Algorithmic Problem ◽  
Complete Problems ◽  
Active Membranes ◽  
Uniform Solution ◽  
Parallel Mode ◽  
The Common ◽  
Np Complete

It is known that the Common Algorithmic Problem (CAP) has a nice property that several other NP-complete problems can be reduced to it in linear time. In the literature, the decision version of this problem can be efficiently solved with a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes that do not use polarizations and present a semi-uniform solution to CAP in the minimally parallel mode.

Performing Balanced Ternary Logic and Arithmetic Operations with Spiking Neural P Systems with Anti-Spikes

2012 ◽  
Vol 505 ◽  
pp. 378-385 ◽  
Author(s):  
Xian Wu Peng ◽  
Xiao Ping Fan ◽  
Jian Xun Liu
Keyword(s):  
Logic Gates ◽  
P Systems ◽  
P System ◽  
Ternary Logic ◽  
Arithmetic Operations ◽  
Spiking Neural P Systems ◽  
Addition And Subtraction ◽  
Distributed And Parallel Computing ◽  
Computing Models ◽  
Natural Way

Spiking neural P systems are a class of distributed and parallel computing models inspired by P systems and spiking neural networks.Spiking neural P system with anti-spikes can encode the balanced ternary three digits in a natural way using three states called anti-spikes, no-input and spikes. In this paper we use this variant of SN P system to simulate universal balanced ternary logic gates including AND,OR and NOT gate and to perform some basic balanced ternary arithmetic operations like addition and subtraction on balanced ternary integers. This paper provides an applicational answer to an open problem formulated by L.Pan and Gh. Păun.

Nonlinear Spiking Neural P Systems

2020 ◽  
Vol 30 (10) ◽  
pp. 2050008 ◽  
Author(s):  
Hong Peng ◽  
Zeqiong Lv ◽  
Bo Li ◽  
Xiaohui Luo ◽  
Jun Wang ◽  
...  
Keyword(s):  
The State ◽  
P Systems ◽  
Number Generator ◽  
Computational Power ◽  
Nonlinear Functions ◽  
Computing Systems ◽  
Spiking Neural P Systems ◽  
System A ◽  
New Variant ◽  
New Type

This paper proposes a new variant of spiking neural P systems (in short, SNP systems), nonlinear spiking neural P systems (in short, NSNP systems). In NSNP systems, the state of each neuron is denoted by a real number, and a real configuration vector is used to characterize the state of the whole system. A new type of spiking rules, nonlinear spiking rules, is introduced to handle the neuron’s firing, where the consumed and generated amounts of spikes are often expressed by the nonlinear functions of the state of the neuron. NSNP systems are a class of distributed parallel and nondeterministic computing systems. The computational power of NSNP systems is discussed. Specifically, it is proved that NSNP systems as number-generating/accepting devices are Turing-universal. Moreover, we establish two small universal NSNP systems for function computing and number generator, containing 117 neurons and 164 neurons, respectively.

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.

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 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.

Spiking Neural P Systems with Extended Channel Rules

2020 ◽  
Vol 31 (01) ◽  
pp. 2050049 ◽  
Author(s):  
Zeqiong Lv ◽  
Tingting Bao ◽  
Nan Zhou ◽  
Hong Peng ◽  
Xiangnian Huang ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Control Mechanism ◽  
P Systems ◽  
Multiple Channels ◽  
Spiking Neural P Systems ◽  
Distributed Parallel Computing ◽  
New Variant ◽  
New Type ◽  
Turing Universality ◽  
Computing Models

This paper discusses a new variant of spiking neural P systems (in short, SNP systems), spiking neural P systems with extended channel rules (in short, SNP–ECR systems). SNP–ECR systems are a class of distributed parallel computing models. In SNP–ECR systems, a new type of spiking rule is introduced, called ECR. With an ECR, a neuron can send the different numbers of spikes to its subsequent neurons. Therefore, SNP–ECR systems can provide a stronger firing control mechanism compared with SNP systems and the variant with multiple channels. We discuss the Turing universality of SNP–ECR systems. It is proven that SNP–ECR systems as number generating/accepting devices are Turing universal. Moreover, we provide a small universal SNP–ECR system as function computing devices.

Time-Free Solution for QSAT by Using Timed Tissue P Systems

2014 ◽  
Vol 568-570 ◽  
pp. 812-816 ◽  
Author(s):  
Yun Yun Niu ◽  
Zhi Gao Wang
Keyword(s):  
Computational Efficiency ◽  
Execution Time ◽  
Realistic Model ◽  
Point Of View ◽  
P Systems ◽  
P System ◽  
Free Solution ◽  
Complete Problem ◽  
Computational Processes ◽  
Tissue P System

A timed tissue P system is constructed by adding a time mapping to the rules of tissue P system to specify the execution time for each rule. It is a more realistic model from a biological point of view. In this study, we investigate the computational efficiency of timed tissue P systems. A uniform and time-free solution to QSAT problem, a famous PSPACE-complete problem, is proposed, where the execution time of the computational processes involved can vary arbitrarily and the output produced is always the same.

A time-free uniform solution to subset sum problem by tissue P systems with cell division

2015 ◽  
Vol 27 (1) ◽  
pp. 17-32 ◽  
Author(s):  
BOSHENG SONG ◽  
TAO SONG ◽  
LINQIANG PAN
Keyword(s):  
Cell Division ◽  
Execution Time ◽  
P Systems ◽  
Subset Sum Problem ◽  
Biological Inspiration ◽  
Global Clock ◽  
Subset Sum ◽  
Uniform Solution ◽  
Hard Problems ◽  
Computing Models

Tissue P systems are a class of bio-inspired computing models motivated by biochemical interactions between cells in a tissue-like arrangement. Tissue P systems with cell division offer a theoretical device to generate an exponentially growing structure in order to solve computationally hard problems efficiently with the assumption that there exists a global clock to mark the time for the system, the execution of each rule is completed in exactly one time unit. Actually, the execution time of different biochemical reactions in cells depends on many uncertain factors. In this work, with this biological inspiration, we remove the restriction on the execution time of each rule, and the computational efficiency of tissue P systems with cell division is investigated. Specifically, we solve subset sum problem by tissue P systems with cell division in a time-free manner in the sense that the correctness of the solution to the problem does not depend on the execution time of the involved rules.

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