# On Controlled P Systems

TL;DR: In this paper, the authors introduce and briefly investigate P systems with controlled computations and compare the relation between the families of sets of numbers computed by the various classes of controlled P systems, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length set of ET0L and of recursively enumerable languages.

Abstract: We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered in each step, all rules used have either the same label, or, possibly, the empty label, λ, then P systems with the computations controlled by languages as in context-free controlled grammars. The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework. A series of open problems and research topics are formulated.

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TL;DR: In this paper, the authors established computational completeness by using specific variants of additional control mechanisms, such as rewriting rules from one set of a finite number of sets of multiset rewriting rules.

Abstract: Whether P systems with only one catalyst can already be computationally complete, is still an open problem. Here we establish computational completeness by using specific variants of additional control mechanisms. At each step using only multiset rewriting rules from one set of a finite number of sets of multiset rewriting rules allows for obtaining computational completeness with one catalyst and only one membrane. If the targets are used for choosing the multiset of rules to be applied, for getting computational completeness with only one catalyst more than one membrane is needed. If the available sets of rules change periodically with time, computational completeness can be obtained with one catalyst in one membrane. Moreover, we also improve existing computational completeness results for P systems with mobile catalysts and for P systems with membrane creation.

17 citations

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25 Jul 2016TL;DR: This work considers the set mode in the cases of taking those sets of rules with the maximal number of applicable rules or with affecting the maximum number of objects.

Abstract: In P systems working in the set derivation mode, even in the maximally parallel derivation mode, rules are only applied in at most one copy in each derivation step. We also consider the set mode in the cases of taking those sets of rules with the maximal number of applicable rules or with affecting the maximal number of objects. For many variants of P systems, the computational completeness proofs even literally still hold true for these new set derivation modes. On the other hand, we obtain new results for P systems using target selection for the rules to be chosen together with these set derivation modes.

16 citations

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01 Mar 2020TL;DR: Besides the standard total halting, this overview paper considers different halting conditions such as unconditional halting and partial halting and explains how the use of different halting Conditions may considerably change the computing power of P systems.

Abstract: In the area of P systems, besides the standard maximally parallel derivation mode, many other derivation modes have been investigated, too. In this overview paper, many variants of hierarchical P systems using different derivation modes are considered and the effects of using different derivation modes, especially the maximally parallel derivation modes and the maximally parallel set derivation modes, on the generative and accepting power are illustrated. Moreover, an overview on some control mechanisms used for P systems is given. Furthermore, besides the standard total halting, we also consider different halting conditions such as unconditional halting and partial halting and explain how the use of different halting conditions may considerably change the computing power of P systems.

12 citations

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01 Dec 2017

TL;DR: Results on the language family generated by the labelled splicing system in comparison with the language families of the Chomsky hierarchy, including recursively enumerable languages, are obtained by involving only either one or two membranes in the P systems considered.

Abstract: Labelled splicing P systems are distributed parallel computing models, where sets of strings that evolve by splicing rules are labelled. In this work, we consider labelled splicing systems with the following modifications: (i) The strings in the membranes are present in arbitrary number of copies; (ii) the rules in the regions are finite in number. Results on the language family generated by the labelled splicing system in comparison with the language families of the Chomsky hierarchy, including recursively enumerable languages, are obtained, by involving only either one or two membranes in the P systems considered.

8 citations

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01 Jan 2018

TL;DR: The objective of this survey is to review and describe the salient features of the major types of array P systems, which have served as the basis for developing other kinds ofarray P systems.

Abstract: A variety of two-dimensional array grammar models generating picture array languages have been introduced and investigated, utilizing and extending the well-established notions and techniques of formal string language theory. On the other hand the versatile computing model with a generic name of P system in the area of membrane computing, has turned out to be a rich framework for different kinds of problems in a variety of fields. Picture array generation in the field of two-dimensional (2D) languages is one such area where P systems with array objects and array rewriting, referred to as array P systems, have been fruitfully employed in increasing the generating power of the 2D grammar models. A variety of array P systems have been proposed in the literature. The objective of this survey is to review and describe the salient features of the major types of array P systems, which have served as the basis for developing other kinds of array P systems. Applications of these array P systems are also briefly described besides indicating possible new directions of investigation.

7 citations

##### References

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Romanian Academy

^{1}TL;DR: It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice.

2,327 citations

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01 Jan 2010

TL;DR: This handbook provides both a comprehensive survey of available knowledge and established research topics, and a guide to recent developments in the field, covering the subject from theory to applications.

Abstract: Part of the broader research field of natural computing, Membrane Computing is an area within computing science that aims to abstract computing ideas and models from the structure and functioning of living cells, as well as from the way the cells are organized in tissues or higher order structures. It studies models of computation (known as P systems) inspired by the biochemistry of cells, in particular by the role of membranes in the compartmentalization of living cells into "protected reactors". This handbook provides both a comprehensive survey of available knowledge and established research topics, and a guide to recent developments in the field, covering the subject from theory to applications. The handbook is suitable both for introducing novices to this area of research, and as a main source of reference for active researchers. It sets out the necessary biological and formal background, with the introductory chapter serving as a gentle introduction to and overview of membrane computing. Individual chapters, written by leading researchers in membrane computing, present the state of the art of all main research trends and include extensive bibliographies.

860 citations

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01 Jan 1989

TL;DR: This book presents 25 different regulating mechanisms by definitions, examples and basic facts, especially concerning hierarchies, as well as selective substitution grammars as one common generalization.

Abstract: It is well-known that context-free grammars cannot cover all aspects of natural languages, progamming languages and other related fields. Therefore a lot of mechanisms have been introduced which control the application of context-free rules. This book presents 25 different regulating mechanisms by definitions, examples and basic facts, especially concerning hierarchies. Matrix, programmed, and random context grammars as typical representants are studied in more detail. Besides their algebraic and decidability properties a comparison is made with respect to syntactic complexity measures and pure versions. Further topics are combinations of some control mechanisms, regulated L systems, automata characterizations, Szilard languages, and grammar forms of regulated grammars as well as selective substitution grammars as one common generalization.

847 citations

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01 Apr 1997171 citations