Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

Gazdag, Zsolt; Kolonits, Gábor

doi:10.1007/978-3-319-54072-6_14

Cited by 5 publications

(3 citation statements)

References 24 publications

(42 reference statements)

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“…Several Turing machine simulations by means of polynomial-time uniform families of P systems have been proposed in the literature; some of these apply to unrestricted Turing machines [26,2], while others are limited to machines working in logarithmic space [25], polynomial time [7,6], polynomial space [32,24,17,10,12,13,15,16,14], or exponential space [1]. Most of these solutions [32,24,1,2,7,17,10,12,13,15,6,16,14] are able to simulate Turing machines working in polynomial time with a polynomial slowdown.…”

Section: Subroutines In Cell-like P Systemsmentioning

confidence: 99%

Subroutines in P systems and closure properties of their complexity classes

Leporati

Manzoni

Mauri

et al. 2020

Theoretical Computer Science

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The literature on membrane computing describes several variants of P systems whose complexity classes C are "closed under exponentiation", that is, they satisfy the inclusion P C ⊆ C, where P C is the class of problems solved by polynomial-time Turing machines with oracles for problems in C. This closure automatically implies closure under many other operations, such as regular operations (union, concatenation, Kleene star), intersection, complement, and polynomial-time mappings, which are inherited from P. Such results are typically proved by showing how elements of a family of P systems Π can be embedded into P systems simulating Turing machines, which exploit the elements of Π as subroutines. Here we focus on the latter construction, abstracting from the technical details which depend on the specific variant of P system, in order to describe a general strategy for proving closure under exponentiation.

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Section: Subroutines In Cell-like P Systemsmentioning

confidence: 99%

Subroutines in P systems and closure properties of their complexity classes

Leporati

Manzoni

Mauri

et al. 2020

Theoretical Computer Science

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“…So far, this conjecture was confirmed only in some special cases, for example, when dissolution rules are not used [11], when the division rules are symmetric [18], or when dissolution and elementary membrane division rules are allowed but both the use of other types of rules and the initial membrane structure are restricted [9,15,34]. The aim to prove Păun's conjecture initiated a research line in membrane computing where the computational power of restricted variants of polarizationless P systems is investigated (see, e.g., [19][20][21], where these P systems with no dissolution rules were studied and [8], where it is shown that these systems can simulate Turing machines efficiently using only evolution and dissolution rules). For a recent survey on exploring the boundary between P and NP in terms of membrane computing, see, e.g., [22].…”

Section: Introductionmentioning

confidence: 99%

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

2021

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It 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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“…It is also widely investigated how certain restrictions on P systems with active membrane affect the computation power of these systems (see for example [6,8,9,11,13,14,16,17,19,20,25]). Probably, the most investigated question in this research line is whether these P systems are still powerful enough to solve hard problems in polynomial time when the polarizations of the membranes are not used.…”

Section: Introductionmentioning

confidence: 99%

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

Gazdag

Kolonits

2019

J Membr Comput

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According to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve-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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Remarks on the Computational Power of Some Restricted Variants of P Systems with Active Membranes

Cited by 5 publications

References 24 publications

Subroutines in P systems and closure properties of their complexity classes

Subroutines in P systems and closure properties of their complexity classes

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

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

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