Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes

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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Solving NP-Complete Problems Using P Systems with Active Membranes

Unconventional Models of Computation, UMC’2K ◽

10.1007/978-1-4471-0313-4_21 ◽

2001 ◽

pp. 289-301 ◽

Cited By ~ 45

Author(s):

Claudio Zandron ◽

Claudio Ferretti ◽

Giancarlo Mauri

Keyword(s):

P Systems ◽

Complete Problems ◽

Active Membranes ◽

Np Complete

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Semi-Uniform Solution for Common Algorithmic Problem by P System in the Minimally Parallel Mode

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.568-570.802 ◽

2014 ◽

Vol 568-570 ◽

pp. 802-806

Author(s):

Yun Yun Niu ◽

Zhi Gao Wang

Keyword(s):

Linear Time ◽

P Systems ◽

P System ◽

Algorithmic Problem ◽

Complete Problems ◽

Active Membranes ◽

Uniform Solution ◽

Parallel Mode ◽

The Common ◽

Np Complete

It is known that the Common Algorithmic Problem (CAP) has a nice property that several other NP-complete problems can be reduced to it in linear time. In the literature, the decision version of this problem can be efficiently solved with a family of recognizer P systems with active membranes with three electrical charges working in the maximally parallel way. We here work with a variant of P systems with active membranes that do not use polarizations and present a semi-uniform solution to CAP in the minimally parallel mode.

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