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 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 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.

scholarly journals Minimal Parallelism and Number of Membrane Polarizations

Triangle ◽  
2018 ◽  
pp. 1
Author(s):  
Artiom Alhazov
Keyword(s):  
P Systems ◽  
Satisfiability Problem ◽  
Main Question ◽  
Efficient Computation ◽  
Active Membranes ◽  
Membrane Division ◽  
Open Question ◽  
Elementary Membrane

It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal.

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.

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.

P SYSTEMS WITH ACTIVE MEMBRANES WORKING IN POLYNOMIAL SPACE

2011 ◽  
Vol 22 (01) ◽  
pp. 65-73 ◽  
Author(s):  
ANTONIO E. PORRECA ◽  
ALBERTO LEPORATI ◽  
GIANCARLO MAURI ◽  
CLAUDIO ZANDRON
Keyword(s):  
Complexity Class ◽  
P Systems ◽  
Polynomial Space ◽  
Active Membranes ◽  
Membrane Division

We prove that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE. This result holds for both confluent and nonconfluent systems, and independently of the use of membrane division rules.

Sign in / Sign up

Export Citation Format

Share Document