A uniform solution to SAT problem by symport/antiport P systems with channel states and membrane division

2018 ◽  
Vol 23 (12) ◽  
pp. 3903-3911 ◽  
Author(s):  
Suxia Jiang ◽  
Yanfeng Wang ◽  
Yansen Su
Keyword(s):  
P Systems ◽  
Sat Problem ◽  
Uniform Solution ◽  
Membrane Division

scholarly journals On Distributed Solution to SAT by Membrane Computing

2018 ◽  
Vol 13 (3) ◽  
pp. 303-320 ◽  
Author(s):  
Henry N. Adorna ◽  
Linqiang Pan ◽  
Bosheng Song
Keyword(s):  
Cell Division ◽  
Computational Models ◽  
P Systems ◽  
Boolean Formula ◽  
Sat Problem ◽  
Complete Problems ◽  
Uniform Solution ◽  
Boolean Formulas ◽  
The Given ◽  
Communication Resource

Tissue P systems with evolutional communication rules and cell division (TPec, for short) are a class of bio-inspired parallel computational models, which can solve NP-complete problems in a feasible time. In this work, a variant of TPec, called $k$-distributed tissue P systems with evolutional communication and cell division ($k\text{-}\Delta_{TP_{ec}}$, for short) is proposed. A uniform solution to the SAT problem by $k\text{-}\Delta_{TP_{ec}}$ under balanced fixed-partition is presented. The solution provides not only the precise satisfying truth assignments for all Boolean formulas, but also a precise amount of possible such satisfying truth assignments. It is shown that the communication resource for one-way and two-way uniform $k$-P protocols are increased with respect to $k$; while a single communication is shown to be possible for bi-directional uniform $k$-P protocols for any $k$. We further show that if the number of clauses is at least equal to the square of the number of variables of the given boolean formula, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem are more efficient than TPec as show in \cite{bosheng2017}; if the number of clauses is equal to the number of variables, then $k\text{-}\Delta_{TP_{ec}}$ for solving the SAT problem work no much faster than TPec.

P systems with proteins: a new frontier when membrane division disappears

2019 ◽  
Vol 1 (1) ◽  
pp. 29-39 ◽  
Author(s):  
David Orellana-Martín ◽  
Luis Valencia-Cabrera ◽  
Agustín Riscos-Núñez ◽  
Mario J. Pérez-Jiménez
Keyword(s):  
P Systems ◽  
New Frontier ◽  
Membrane Division

A Solution for All-SAT Problem Based on P Systems

2016 ◽  
Vol 13 (7) ◽  
pp. 4293-4301 ◽  
Author(s):  
Wei Song ◽  
Ping Guo ◽  
HaiZhu Chen
Keyword(s):  
P Systems ◽  
Sat Problem

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.

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.

scholarly journals Bio-inspired Membrane Operations in P Systems with Active Membranes

Triangle ◽  
2018 ◽  
pp. 19
Author(s):  
Artiom Alhazov ◽  
Tseren-Onolt Ishdorj
Keyword(s):  
General Class ◽  
Membrane Structure ◽  
Membrane Separation ◽  
Linear Time ◽  
P Systems ◽  
Sat Problem ◽  
Separation Membrane ◽  
Active Membranes

In this paper we define a general class of P systems covering some biological operations with membranes, including evolution, communication, and modifying the membrane structure, and we describe and formally specify some of these operations: membrane merging, membrane separation, membrane release. We also investigate a particular combination of types of rules that can be used in solving the SAT problem in linear time.

scholarly journals A new method to simulate restricted variants of polarizationless P systems with active membranes

2019 ◽  
Vol 1 (4) ◽  
pp. 251-261 ◽  
Author(s):  
Zsolt Gazdag ◽  
Gábor Kolonits
Keyword(s):  
Membrane Structure ◽  
P Systems ◽  
New Approach ◽  
Complete Problems ◽  
Active Membranes ◽  
Special Cases ◽  
Division Polynomials ◽  
Initial Membrane ◽  
Membrane Division ◽  
Elementary Membrane

AbstractAccording to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve $${\mathbf {NP}}$$NP-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

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