Characterising the complexity of tissue P systems with fission rules

Leporati, Alberto; Manzoni, Luca; Mauri, Giancarlo; Porreca, Antonio E.; Zandron, Claudio

doi:10.1016/j.jcss.2017.06.008

Cited by 20 publications

(17 citation statements)

References 14 publications

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“…The results in [24] improve previously known upper bound PSPACE on the power of tissue P systems reported in [60,61]. The authors of [24] conjecture that the class PSPACE can still be reached when one assumes non-deterministic non-confluent tissue P systems, that is, allowing the same tissue P system to have both accepting and rejecting computations, with the final result determined by the existence of at least one accepting computation. A similar result has been already shown for the case of non-confluent active membrane systems of depth 1, see Sect.…”

Section: S E P a R A T I O N R U L E S : [A]supporting

confidence: 70%

“…Finally, the class PSPACE was shown to be the upper bound for several models of P systems [61,62,64], the question remaining open in the other cases. This upper bound was shown to be tight in some cases, while some other models have been recently reported to characterize the class # , defined by means of oracles for counting problems [22,24]. Note the use of oracles and complexity classes of the form , containing languages recognizable by polynomial-time Turing machines with oracles for languages in .…”

Section: Introductionmentioning

confidence: 90%

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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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Section: S E P a R A T I O N R U L E S : [A]supporting

confidence: 70%

Section: Introductionmentioning

confidence: 90%

P systems attacking hard problems beyond NP: a survey

Sosík

2019

J Membr Comput

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“…The idea to attack computationally hard problems by means of P systems has been introduced quite early in the area of Membrane Computing, by considering the idea of active membranes [28]: new membranes are generated from existing ones through membrane division (mimicking the mitosis process), and then used in parallel to solve problems in or even in . Allowing or forbidding the use of some features, or considering different organizations of the membranes, results in systems of a different computational efficiency (see, e.g., [5,8,9,16,24,34,39,41,45,46]). Anyhow, this is not always the case: the use of some features can be considered (like, e.g.…”

Section: Introductionmentioning

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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“…For example, nesting of non-deterministic machines (where the non-determinism was simulated by membrane division) and a counting mechanism allows to characterize P #P , the class of all problems solvable by a deterministic TM with access to a #P oracle [1,3]. The same ideas can be applied to tissue P systems [4], where the different communication topology makes even more important to keep TM simulations compact [2].…”

Section: Introductionmentioning

confidence: 99%

A Turing machine simulation by P systems without charges

et al. 2020

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It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class P by leveraging the uniformity condition. Here we show that these systems are indeed able to simulate deterministic Turing machines working in polynomial time with a weaker uniformity condition and using only one level of membrane nesting. This allows us to embed this construction into more complex membrane structures, possibly showing that constructions similar to the one performed in [1] for P systems with charges can be carried out also in this case.

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Characterising the complexity of tissue P systems with fission rules

Cited by 20 publications

References 14 publications

P systems attacking hard problems beyond NP: a survey

P systems attacking hard problems beyond NP: a survey

Bounding the space in P systems with active membranes

A Turing machine simulation by P systems without charges

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