An Efficient Simulation of Polynomial-Space Turing Machines by P Systems with Active Membranes

Valsecchi, Andrea; Porreca, Antonio E.; Leporati, Alberto; Mauri, Giancarlo; Zandron, Claudio

doi:10.1007/978-3-642-11467-0_31

Cited by 11 publications

(3 citation statements)

References 17 publications

(19 reference statements)

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“…In [42], it was shown that a deterministic Turing machine working in polynomial space, with respect to the input length, can be efficiently simulated (both in terms of time and space) by a semi-uniform family of P systems with active membranes, using only communication rules.…”

Section: Proposition 4 ⊆ Ndiss Eammentioning

confidence: 99%

Evaluating space measures in P systems

Leporati¹,

Manzoni²,

Mauri³

et al. 2022

J Membr Comput

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P systems with active membranes are a variant of P systems where membranes can be created by division of existing membranes, thus creating an exponential amount of resources in a polynomial number of steps. Time and space complexity classes for active membrane systems have been introduced, to characterize classes of problems that can be solved by different membrane systems making use of different resources. In particular, space complexity classes introduced initially considered a hypothetical real implementation by means of biochemical materials, assuming that every single object or membrane requires some constant physical space (corresponding to unary notation). A different approach considered implementation of P systems in silico, allowing to store the multiplicity of each object in each membrane using binary numbers. In both cases, the elements contributing to the definition of the space required by a system (namely, the total number of membranes, the total number of objects, the types of different membranes, and the types of different objects) was considered as a whole. In this paper, we consider a different definition for space complexity classes in the framework of P systems, where each of the previous elements is considered independently. We review the principal results related to the solution of different computationally hard problems presented in the literature, highlighting the requirement of every single resource in each solution. A discussion concerning possible alternative solutions requiring different resources is presented.

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Section: Proposition 4 ⊆ Ndiss Eammentioning

confidence: 99%

Evaluating space measures in P systems

Leporati¹,

Manzoni²,

Mauri³

et al. 2022

J Membr Comput

Self Cite

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show abstract

“…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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“…Known results of AM systems with polarizations reported in [3,22,44,46,47,62,66] are summarized in Table 1, with respect to various types of (dis)allowed rules the P system can use. Each column in the table defines a specific combination of allowed types of rules, and the last row displays the resulting class of problems solvable by uniform families of AM systems using only these kinds of rules.…”

Section: P Systems With Active Membranesmentioning

confidence: 99%

P systems attacking hard problems beyond NP: a survey

Sosík

2019

J Membr Comput

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In the field of membrane computing, a great attention is traditionally paid to the results demonstrating a theoretical possibility to solve NP-complete problems in polynomial time by means of various models of P systems. A bit less common is the fact that almost all models of P systems with this capability are actually stronger: some of them are able to solve PSPACEcomplete problems in polynomial time, while others have been recently shown to characterize the class # (which is conjectured to be strictly included in PSPACE). A large part of these results has appeared quite recently. In this survey, we focus on strong models of membrane systems which have the potential to solve hard problems belonging to classes containing NP. These include P systems with active membranes, P systems with proteins on membranes and tissue P systems, as well as P systems with symport/antiport and membrane division and, finally, spiking neural P systems. We provide a survey of computational complexity results of these membrane models, pointing out some features providing them with their computational strength. We also mention a sequence of open problems related to these topics.

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An Efficient Simulation of Polynomial-Space Turing Machines by P Systems with Active Membranes

Cited by 11 publications

References 17 publications

Evaluating space measures in P systems

Evaluating space measures in P systems

Subroutines in P systems and closure properties of their complexity classes

P systems attacking hard problems beyond NP: a survey

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