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.

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.

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.

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.

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.

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.

A uniform family of tissue P systems with protein on cells solving 3-coloring in linear time

2016 ◽  
Vol 17 (2) ◽  
pp. 311-319 ◽  
Author(s):  
A. Hepzibah Christinal ◽  
Daniel Díaz-Pernil ◽  
T. Mathu
Keyword(s):  
Linear Time ◽  
P Systems

Diagnosability and Diagnostic Algorithm for Pancake Graph under the Comparison Model

2015 ◽  
Vol 15 (01n02) ◽  
pp. 1550005
Author(s):  
WENJUN LIU ◽  
CHENG-KUAN LIN
Keyword(s):  
Fault Diagnosis ◽  
Interconnection Networks ◽  
Linear Time ◽  
Hamiltonian Path ◽  
Diagnostic Algorithm ◽  
Efficient Algorithms ◽  
Comparison Model ◽  
Diagnosis Model

Fault diagnosis is important for the reliability of interconnection networks. This paper addresses the fault diagnosis of n-dimensional pancake graph Pn under the comparison diagnosis model. By the concept of local diagnosability, we first prove that the diagnosabitly of Pn is n − 1, and it has strong local diagnosability property even if there are n − 3 faulty edges. Furthermore, we present efficient algorithms to locate extended star and Hamiltonian path structures in Pn, respectively. According to the works of Li et al. and Lai, the extended star and Hamiltonian path structures can be used to identify all faulty vertices in linear time, provided the number of faulty vertices is no more than n − 1.

DNA Computing

2010 ◽  
Vol 2 (4) ◽  
pp. 12-37
Author(s):  
Tao Song ◽  
Xun Wang ◽  
Shudong Wang ◽  
Yun Jiang
Keyword(s):  
Dna Computing ◽  
Medical Science ◽  
Theoretical Framework ◽  
Biomolecular Computing ◽  
Dna Encoding ◽  
Research Directions ◽  
Hamilton Path ◽  
Complete Problems ◽  
Intractable Problems ◽  
Computing Models

DNA computing is widely accepted as a new computing framework all over the world. In this chapter, the background of DNA computing is firstly introduced by solving a Hamilton Path problem. Then three research directions are proposed according to the current development of it, including the theoretical framework, practical DNA computing models and DNA encoding. In each part of the three research directions, many recent results are involved. In the theoretical framework, DNA computing is proved to be computationally universal by four formal DNA computing models. In practical DNA computing models, DNA computing is shown to solve NP-complete problems and work well in other fields, such as medical science. In DNA encoding, some DNA codes and encoding methods are introduced to avoid the false positive phenomenon. And they have a final purpose in common: constructing a universal Biomolecular computing model, which is also called as biomolecular computer, to solve intractable problems for electrical computers. Finally, some further research directions are shown in each part for the design of biomolecular computer.

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