Minimal Parallelism and Number of Membrane Polarizations

Triangle ◽

10.17345/triangle6.1-17 ◽

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.

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On the power of P systems with active membranes using weak non-elementary membrane division

Journal of Membrane Computing ◽

10.1007/s41965-021-00082-2 ◽

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.

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

Journal of Membrane Computing ◽

10.1007/s41965-019-00024-z ◽

2019 ◽

Vol 1 (4) ◽

pp. 251-261 ◽

Cited By ~ 3

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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Elementary Active Membranes Have the Power of Counting

Natural Computing for Simulation and Knowledge Discovery ◽

10.4018/978-1-4666-4253-9.ch013 ◽

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.

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Elementary Active Membranes Have the Power of Counting

International Journal of Natural Computing Research ◽

10.4018/jncr.2011070104 ◽

2011 ◽

Vol 2 (3) ◽

pp. 35-48 ◽

Cited By ~ 12

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

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P SYSTEMS WITH ACTIVE MEMBRANES WORKING IN POLYNOMIAL SPACE

International Journal of Foundations of Computer Science ◽

10.1142/s0129054111007836 ◽

2011 ◽

Vol 22 (01) ◽

pp. 65-73 ◽

Cited By ~ 12

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.

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