A Computational Complexity Theory in Membrane Computing

Pérez–Jiménez, Mario J.

doi:10.1007/978-3-642-11467-0_10

Cited by 28 publications

(17 citation statements)

References 26 publications

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“…To solve decision problems (i.e., decide languages over an alphabet ), we use families of recognizer P systems = { x ∶ x ∈ ⋆ } , as commonly done in the framework of Membrane Computing when one considers semiuniform solutions ( [30]). Given an input x, we consider a specific P system x that decides the membership of x in the language L ⊆ ⋆ by accepting or rejecting.…”

Section: Definition 1 a P System With Active Membranes Having Ini-mentioning

confidence: 99%

Bounding the space in P systems with active membranes

Zandron

2020

J Membr Comput

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P systems with active membranes have been widely used to attack problems in or even in ; in general, an exponential amount of space is generated in polynomial time by dividing existing membranes. Natural questions arise in this framework, concerning the power of P systems when different bounds are considered for the use of the space resource. We consider in this paper two natural bounds: the amount of available physical space (in terms of the number of objects and membranes) and the organization of the membrane structure (in particular, concerning the depth of the membrane structure). We present the main results obtained so far on this subject.

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Section: Definition 1 a P System With Active Membranes Having Ini-mentioning

confidence: 99%

Bounding the space in P systems with active membranes

Zandron

2020

J Membr Comput

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“…Analogously, a family = { (n) ∶ n ∈ ℕ} of recognizer P systems with input membrane, solving X in a uniform way, has been defined. The reader is referred to [43] for more details.…”

Section: Definition 3 ([43]mentioning

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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“…Some of these models (see [5,8], for instance) were shown to be complete by simulating, in a massively parallel manner, all the possible computations of a nondeterministic Turing machine; characterizations of several complexity classes, like NP, P and PSPACE, were obtained in this framework. However, these machines were, generally, used to accept languages, not to decide them; in the case when a deciding model was considered ( [5]), the rejecting condition was just a mimic of the rejecting condition from classical computing models.…”

Section: Introductionmentioning

confidence: 99%

Deciding According to the Shortest Computations

Manea

2011

Models of Computation in Context

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In this paper we propose, and analyze from the computational complexity point of view, a new variant of nondeterministic Turing machines. Such a machine accepts a given input word if and only if one of its shortest possible computations on that word is accepting; on the other hand, the machine rejects the input word when all the shortest computations performed by the machine on that word are rejecting. Our main results are two new characterizations of P NP [log] and P NP in terms of the time complexity classes defined for such machines.

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A Computational Complexity Theory in Membrane Computing

Cited by 28 publications

References 26 publications

Bounding the space in P systems with active membranes

Bounding the space in P systems with active membranes

P systems attacking hard problems beyond NP: a survey

Deciding According to the Shortest Computations

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