scholarly journals Tissue P Systems with Cell Division

2008 ◽  
Vol 3 (3) ◽  
pp. 295 ◽  
Author(s):  
Gheorghe Păun ◽  
Mario J. Perez-Jimenez ◽  
Agustín Riscos-Nunez
Keyword(s):  
Cell Division ◽  
Polynomial Time ◽  
Basic Feature ◽  
P Systems ◽  
Sat Problem ◽  
Active Membranes ◽  
Hard Problems

In tissue P systems several cells (elementary membranes) communicate through symport/antiport rules, thus carrying out a computation. We add to such systems the basic feature of (cell–like) P systems with active membranes – the possibility to divide cells. As expected (as it is the case for P systems with active membranes), in this way we get the possibility to solve computationally hard problems in polynomial time; we illustrate this possibility with SAT problem.

scholarly journals Elementary Active Membranes Have the Power of Counting

2014 ◽  
pp. 194-206
Author(s):  
Antonio E. Porreca ◽  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Claudio Zandron
Keyword(s):  
Polynomial Time ◽  
P Systems ◽  
Decision Problems ◽  
Active Membranes ◽  
Hard Problems ◽  
Whole Class ◽  
Uniformity Condition ◽  
Membrane Division

P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one.

scholarly journals Elementary Active Membranes Have the Power of Counting

2011 ◽  
Vol 2 (3) ◽  
pp. 35-48 ◽  
Author(s):  
Antonio E. Porreca ◽  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Claudio Zandron
Keyword(s):  
Polynomial Time ◽  
P Systems ◽  
Decision Problems ◽  
Active Membranes ◽  
Hard Problems ◽  
Whole Class ◽  
Uniformity Condition ◽  
Membrane Division

P systems with active membranes have the ability of solving computationally hard problems. In this paper, the authors prove that uniform families of P systems with active membranes operating in polynomial time can solve the whole class of PP decision problems, without using nonelementary membrane division or dissolution rules. This result also holds for families having a stricter uniformity condition than the usual one.

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 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.

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.

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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