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Journal Article

On the Power of P Systems with Contextual Rules

01 Jan 2002-Fundamenta Informaticae (IOS Press)-Vol. 49, Iss: 1, pp 167-178
TL;DR: P Systems with string objects which evolve by means of one-sided contextual rules and erasing contextual rules are considered, and it is shown that systems with three membranes characterize the family of recursively enumerable languages.
Abstract: We consider P Systems with string objects which evolve by means of one-sided contextual rules and erasing contextual rules. The generative power of these systems with three or less than three membranes is investigated. We show that systems with three membranes characterize the family of recursively enumerable languages. When the string replication is used in one-sided contextual rules, these systems are able of solving NP-complete problems in linear time: this is exemplified with SAT and HPP.
Citations
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Book ChapterDOI
TL;DR: This work investigates a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction, and shows that for such systems with only one membrane and using only singleton activator and prohibitor sets, universal computational power is obtained.
Abstract: We investigate a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction; however, the permeability of a channel can be controlled by multisets of prohibitors, too.We will show that for such systems with only one membrane and using only singleton activator and prohibitor sets, we already obtain universal computational power. When using systems with activating multisets for membrane channels only, we obtain a similar result. By showing a close correspondence to P systems with symport/antiport as introduced in [13] we can optimize some results given there.

47 citations


Cites background from "On the Power of P Systems with Cont..."

  • ...Contextual grammars for processing string-objects in P systems were considered in [7, 5 ], where the derivations are taking place depending upon the contexts....

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Gheorghe P1
01 Jan 2007
TL;DR: The present notes intend to survey the research related to some of the problems of membrane computing, mentioning both progresses made in solving them and questions which still wait for research efiorts.
Abstract: Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of the living cell, and from the way cells cooperate in tissues, organs, or other populations of cells. This research area developed very fast, both at the theoretical level and in what concerns the applications. During the almost ten years since membrane computing was initiated, several open problems were circulated, sometimes in comprehensive lists prepared for meetings in this area. The present notes intend to survey the research related to some of these problems, mentioning both progresses made in solving them and questions which still wait for research efiorts.

26 citations


Cites background from "On the Power of P Systems with Cont..."

  • ..., [33], [34]), in several cases dealing with array languages, for the other two questions we are not aware of any paper addressing them....

    [...]

Journal Article
TL;DR: This paper improves a universality result avoiding the extended feature and by using rules of small weight in contextual P systems and has two (rather surprising) universality results, both of them using three membranes for non-extended systems with replicated rewriting and with leftmost rewriting.
Abstract: In this paper, we continue the study of contextual and rewriting P systems. In contextual P systems, we improve a universality result avoiding the extended feature and by using rules of small weight. In rewriting P systems, we have two (rather surprising) universality results, both of them using three membranes, for non-extended systems with replicated rewriting and with leftmost rewriting, respectively.

7 citations


Cites background from "On the Power of P Systems with Cont..."

  • ...Variants of P systems with string objects [5, 3] using contextual rules [9] have also been investigated extensively....

    [...]

Journal ArticleDOI
TL;DR: This work considers a P system with only alphabetic flat splicing rules as the evolution rules and strings of symbols as objects in its regions and shows that AFS P systems with two membranes are more powerful in generative power than AFSP systems with a single membrane.

6 citations


Cites background from "On the Power of P Systems with Cont..."

  • ...In [14], a hybrid variety of language generating P systems that make use of both context-free and contextadjoining rules, is dealt with while in [15], the generative power of P systems with string-objects and contextual rules was investigated....

    [...]

Book ChapterDOI
28 Aug 2012
TL;DR: It is shown that the set of valid SAT- formulae and n-SAT-formulae over finite sets of variables are regular languages, and theoretically the words of the SAT languages can be accepted in linear time with respect to their lengths by a traditional computer.
Abstract: There are several papers in which SAT is solved in linear time by various new computing paradigms, and specially by various membrane computing systems. In these approaches the used alphabet depends on the number of variables. That gives different classes of the problem by the number of the variables. In this paper we show that the set of valid SAT-formulae and n-SAT-formulae over finite sets of variables are regular languages. We show a construction of deterministic finite automata which accept the SAT and n-SAT languages in conjunctive normal form checking both their syntax and satisfiable evaluations. Thus, theoretically the words of the SAT languages can be accepted in linear time with respect to their lengths by a traditional computer.

6 citations

References
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Journal ArticleDOI
Gheorghe Paun1
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

Journal Article
TL;DR: It is proved that a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects, is not only computationally universal, but also able to solve NP complete problems in polynomial time.
Abstract: P systems are parallel Molecular Computing models based on processing multisets of objects in cell-like membrane structures. Various variants were already shown to be computationally universal, equal in power to Turing machines. In this paper one proposes a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects. Moreover, the membranes can multiply themselves by division. We prove that this variant is not only computationally universal, but also able to solve NP complete problems in polynomial (actually, linear) time. We exemplify this assertion with the well-known SAT problem.

366 citations

Book
01 Jan 1997
TL;DR: 1. Origin and Motivation, Formal Language Theory Prerequisites, and A Generalization: n-Contextual Grammars.
Abstract: 1. Origin and Motivation. 2. Formal Language Theory Prerequisites. 3. Contexts (Adjoining) Everywhere. 4. Basic Classes of Contextual Grammars. 5. Generative Capacity. 6. Language Theoretic Properties. 7. Linguistically Relevant Properties. 8. Grammars with Restricted Selection. 9. Grammars with Minimal/Maximal Use of Selectors. 10. Variants of Contextual Grammars. 11. Two-Level Contextual Grammars. 12. Regulated Contextual Grammars. 13. A Generalization: n-Contextual Grammars. 14. A Dual Model: Insertion Grammars. 15. Further Topics. 16. Open Problems and Research Topics. Bibliography. Subject Index.

179 citations

Proceedings ArticleDOI
01 Sep 1969
TL;DR: Every finite sequence of elements in ia called a vocnbuV is said to be a s t r i n g o n V, which is a finite set of strings on the vocabulary V~ and let@be a finite se@ of contexts on V.

84 citations