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Journal ArticleDOI

Contextual array P systems

01 Aug 2004-International Journal of Computer Mathematics (Taylor & Francis)-Vol. 81, Iss: 8, pp 955-969
TL;DR: The relation between external arrays contextual P systems and external array contextual grammars with regular control is obtained and some properties of these systems are discussed.

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Abstract: We define external and internal array contextual P systems, which generate rectangular arrays. We also introduce external array contextual P systems with erased contexts. Some properties of these systems are discussed. We obtain the relation between external array contextual P systems and external array contextual grammars with regular control.

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Citations
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Journal ArticleDOI
19 Aug 2003-Natural Computing
TL;DR: It is proved that the P systems with context-free rules are computationally universal, able to generate all computable array languages.

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Abstract: We consider array languages (sets of pictures consisting of symbols placed in the lattice points of the 2D grid) and the possibility to handle them with P systems. After proving binary normal forms for array matrix grammars (which, even in the case when no appearance checking is used, are known to generate the array languages of arbitrary array grammars), we prove that the P systems with context-free rules (with three membranes and no control on the communication or the use of rules) are computationally universal, able to generate all computable array languages. Some open problems are also formulated.

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82 citations


Journal ArticleDOI
TL;DR: A parallel implementation of a new algorithm for segmenting images with gradient-based edge detection by using techniques from Natural Computing, implemented in a novel device architecture called CUDA(TM)(Compute Unified Device Architecture).

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Abstract: In this paper, we present a parallel implementation of a new algorithm for segmenting images with gradient-based edge detection by using techniques from Natural Computing. This bio-inspired parallel algorithm has been implemented in a novel device architecture called CUDA(TM)(Compute Unified Device Architecture). The implementation has been designed via tissue P systems on the framework of Membrane Computing. Some examples and experimental results are also presented.

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52 citations


01 Jan 2012-
Abstract: This is a list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France (23 26 August 2011), meant initially to be a working material for Tenth Brainstorming Week on Membrane Computing, Sevilla, Spain (January 30 February 3, 2012). The result was circulated in several versions before the brainstorming and then modified according to the discussions held in Sevilla and according to the progresses made during the meeting. In the present form, the list gives an image about key research directions currently active in membrane computing.

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45 citations


Journal ArticleDOI
TL;DR: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.

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Abstract: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.

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42 citations


Journal ArticleDOI
01 Mar 2019-
TL;DR: Some of the open research lines in the area of membrane computing are presented, focusing on segmentation problems, skeletonization and algebraic-topological aspects of the images.

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Abstract: Membrane computing is a well-known research area in computer science inspired by the organization and behavior of live cells and tissues. Their computational devices, called P systems, work in parallel and distributed mode and the information is encoded by multisets in a localized manner. All these features make P systems appropriate for dealing with digital images. In this paper, some of the open research lines in the area are presented, focusing on segmentation problems, skeletonization and algebraic-topological aspects of the images. An extensive bibliography about the application of membrane computing to the study of digital images is also provided.

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40 citations


References
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Journal ArticleDOI
Gheorghe Paun1Institutions (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.

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Abstract: We introduce a new computability model, of a distributed parallel type, based on the notion of a membrane structure. Such a structure consists of several cell-like membranes, recurrently placed inside a unique “skin” membrane. A plane representation is a Venn diagram without intersected sets and with a unique superset. In the regions delimited by the membranes there are placed objects. These objects are assumed to evolve: each object can be transformed in other objects, can pass through a membrane, or can dissolve the membrane in which it is placed. A priority relation between evolution rules can be considered. The evolution is done in parallel for all objects able to evolve. In this way, we obtain a computing device (we call it a P system): start with a certain number of objects in a certain membrane and let the system evolve; if it will halt (no object can further evolve), then the computation is finished, with the result given as the number of objects in a specified membrane. If the development of the system goes forever, then the computation fails to have an output. We prove 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. In fact, we do not need cooperating rules, but we only use catalysts, specified objects which are present in the rules but are not modified by the rule application. One catalyst suffices. A variant is also considered, with the objects being strings over a given alphabet. The evolution rules are now based on string transformations. We investigate the case when either the rewriting operation from Chomsky grammars (with respect to context-free productions) or the splicing operation from H systems investigated in the DNA computing is used. In both cases, characterizations of recursively enumerable languages are obtained by very simple P systems: with three membranes in the rewriting case and four in the splicing case. Several open problems and directions for further research are formulated

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2,182 citations


"Contextual array P systems" refers background in this paper

  • ...r0 = I1r1 + I2r2 + · · · + Imrm + λ (1) ri = Hiri + Oir0, 1 ≤ i ≤ m (2) R = O0r0 (3)...

    [...]

  • ...Case(1): Suppose R = a, where a is a symbol representing a contextual rule in G....

    [...]


Book
01 Jan 1968-

1,177 citations


Journal ArticleDOI
01 Oct 1983-

236 citations


"Contextual array P systems" refers background in this paper

  • ...r0 = I1r1 + I2r2 + · · · + Imrm + λ (1) ri = Hiri + Oir0, 1 ≤ i ≤ m (2) R = O0r0 (3)...

    [...]

  • ...Case(3): Suppose R = r1r2, where r1 and r2 are regular expressions....

    [...]

  • ...0 ≤ i ≤ m. Ij is the set of all rules with target inj , Oj is the set of all rules with target out in membrane j and Hj is the set of all rules with target here in membrane j. r0 = I1r1 + I2r2 + · · · + Imrm + λ (1) ri = Hiri + Oir0, 1 ≤ i ≤ m (2) R = O0r0 (3) Equation (2) implies ri = H i Oir0 (4) Now, from Eq....

    [...]


Book
01 Jan 1979-

179 citations


"Contextual array P systems" refers background in this paper

  • ...(1) r0 = m∑ i=1 Iiri + λ = m∑ i=1 IiH i Oir0 + λ Therefore, r0 = ( m∑ i=1 IiH i Oi ) R = r0O0 = ( m∑ i=1 IiH i Oi ) O0 Hence the Theorem....

    [...]

  • ...Case(4): Suppose R = r , where r is a regular expression....

    [...]

  • ...Equation (2) implies ri = H i Oir0 (4)...

    [...]

  • ...0 ≤ i ≤ m. Ij is the set of all rules with target inj , Oj is the set of all rules with target out in membrane j and Hj is the set of all rules with target here in membrane j. r0 = I1r1 + I2r2 + · · · + Imrm + λ (1) ri = Hiri + Oir0, 1 ≤ i ≤ m (2) R = O0r0 (3) Equation (2) implies ri = H i Oir0 (4) Now, from Eq....

    [...]


Journal ArticleDOI
TL;DR: Generative models of picture languages with array rewriting rules are presented and each letter of the alphabet of different sizes can be generated by a context-free array grammar.

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Abstract: Generative models of picture languages with array rewriting rules are presented. The rewriting rules are regular, context-free or context-sensitive with arrays of terminals in the place of strings of terminals. Derivations are restricted by the condition for row and column catenation. The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. A distinct hierarchy is shown to exist between the different classes introduced. The models are closed under reflection (about base and rightmost vertical), halfturn, quarter-turn, transpose, and conjugation. Further closure properties such as union, product, star and homomorphism are examined. The models can be applied to generate several interesting patterns of kolam and to describe the repetitive patterns of two-dimensional crystallography. Each letter of the alphabet of different sizes can be generated by a context-free array grammar.

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127 citations


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