Bounding the space in P systems with active membranes

Zandron, Claudio

doi:10.1007/s41965-020-00039-x

Cited by 11 publications

(6 citation statements)

References 44 publications

(57 reference statements)

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“…The refinement of these techniques has supported the demonstration of several new frontiers of efficiency. Apart from these techniques, other techniques have been used both in demonstrating the computational power [5] and the computational efficiency [10,28] can be found in the literature. However, due to the restriction of length of the work it would be impossible to include them all.…”

Section: Discussionmentioning

confidence: 99%

Proof techniques in Membrane Computing

Orellana-Martín

Valencia-Cabrera

Pérez–Jiménez

2021

Theoretical Computer Science

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From the creation of the field of Membrane Computing in 1998, several research lines have been opened. On the one hand, theoretical questions like the computational power and the computational efficiency of P systems have been studied. In this sense, several techniques to demonstrate the ability of these systems to provide solutions to computational problems have been explored. The study of efficient (polynomial-time) solutions to presumably hard problems for finding thin frontiers of efficiency is a very active area. On the other hand, several applications in biology, ecology, economy, robotics and fault diagnosis, among others, have been investigated. Real systems with some characteristics seem to be easy to model with membrane systems due to their behaviour. In this work, a survey of the theoretical part will be given, explaining techniques both in the field of computability theory and in the field of computational complexity theory.

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Section: Discussionmentioning

confidence: 99%

Proof techniques in Membrane Computing

Orellana-Martín

Valencia-Cabrera

Pérez–Jiménez

2021

Theoretical Computer Science

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“…The relations between standard computational complexity classes and the space complexity classes defined in these terms have been studied, both when at least a linear amount of space is used [30,31], as well as when only sublinear [32] or even constant amount of space [15] is available. A recent survey concerning results obtained by considering different bounds on space can be found in [39].…”

Section: Introductionmentioning

confidence: 99%

Alternative space definitions for P systems with active membranes

et al. 2021

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The first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane requires some constant physical space. This is equivalent to using a unary encoding to represent multiplicities for each object and membrane. A different approach can also be considered, having in mind an implementation of P systems in silico; in this case, the multiplicity of each object in each membrane can be stored using binary numbers, thus reducing the amount of needed space. In this paper, we give a formal definition for this alternative space complexity measure, we define the corresponding complexity classes and we compare such classes both with standard space complexity classes and with complexity classes defined in the framework of P systems considering the original definition of space.

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“…, where e 0 , e 1 , e 2 are polarizations (see also [2,36], where the space complexity of P systems employing weak non-elementary membrane division rules is discussed). Let us note here that, to the best of our knowledge, it is not known whether weak non-elementary membrane division rules are indeed weaker than strong nonelementary membrane division rules.…”

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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Bounding the space in P systems with active membranes

Cited by 11 publications

References 44 publications

Proof techniques in Membrane Computing

Proof techniques in Membrane Computing

Alternative space definitions for P systems with active membranes

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

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