Shallow laconic P systems can count

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

doi:10.1007/s41965-020-00032-4

Cited by 8 publications

(5 citation statements)

References 7 publications

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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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“…In [8,11], solutions for the SAT problem are proposed which use different strategies than previously proposed solutions. Systems of a shallow depth are the subject of [20][21][22]. A recent survey on different strategies to approach computationally hard problems by P systems with active membranes can be found in [39].…”

Section: Introductionmentioning

confidence: 99%

Evaluating space measures in P systems

et al. 2022

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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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“…In [7,10] solutions for SAT are proposed which use different strategies than previously proposed solutions. Systems of a shallow depth are the subject of [17][18][19]. A recent survey on different strategies to approach computationally hard problems by P systems with active membranes can be found in [36].…”

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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Shallow laconic P systems can count

Cited by 8 publications

References 7 publications

Proof techniques in Membrane Computing

Proof techniques in Membrane Computing

Evaluating space measures in P systems

Alternative space definitions for P systems with active membranes

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