Contextual array P systems

doi:10.1080/00207160410001684343

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Contextual array P systems

Journal Article•DOI•

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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Journal Article•DOI•

Array-rewriting P systems

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Rodica Ceterchi¹, Madhu Mutyam², Gheorghe Paun¹, K. G. Subramanian³•Institutions (3)

Rovira i Virgili University¹, Indian Institute of Technology Madras², Madras Christian College³

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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84 citations

Journal Article•DOI•

Membrane computing and image processing: a short survey

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Daniel Díaz-Pernil¹, Miguel A. Gutiérrez-Naranjo¹, Hong Peng²•Institutions (2)

University of Seville¹, Xihua University²

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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64 citations

Journal Article•DOI•

Segmenting images with gradient-based edge detection using Membrane Computing

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Daniel Díaz-Pernil¹, Ainhoa Berciano², Francisco Peña-Cantillana¹, Miguel A. Gutiérrez-Naranjo¹•Institutions (2)

University of Seville¹, University of the Basque Country²

01 Jun 2013-Pattern Recognition Letters

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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57 citations

Journal Article•DOI•

Research frontiers of membrane computing: open problems and research topics

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Marian Gheorghe¹, Gheorghe Păun², Gheorghe Păun³, Mario J. Pérez-Jiménez³, Grzegorz Rozenberg⁴, Grzegorz Rozenberg⁵ - Show less +2 more•Institutions (5)

University of Sheffield¹, Romanian Academy², University of Seville³, Leiden University⁴, University of Colorado Boulder⁵

24 Oct 2013-International Journal of Foundations of Computer Science

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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47 citations

Frontiers of Membrane Computing: Open Problems and Research Topics

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Marian Gheorgue, Gheorghe Paun, Mario de Jesús Pérez Jiménez

01 Jan 2012

TL;DR: A list of open problems and research topics collected after the Twelfth Conference on Membrane Computing, CMC 2012 (Fontainebleau, France) was meant initially to be a working material for the Tenth Brainstorming Week on MEMBRANE Computing, Sevilla, Spain (January 30 February 3, 2012) as mentioned in this paper.

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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

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Journal Article•DOI•

Computing with Membranes

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Gheorghe Paun¹•Institutions (1)

Romanian Academy¹

01 Aug 2000-Journal of Computer and System Sciences

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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2,327 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)...
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...Case(1): Suppose R = a, where a is a symbol representing a contextual rule in G....
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Book•

Syntactic pattern recognition and applications

[...]

King-Sun Fu

01 Jan 1968

1,178 citations

Journal Article•DOI•

Syntactic pattern recognition and applications

[...]

O. Firschein

01 Oct 1983

242 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....
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...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....
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Book•

Picture languages: Formal models for picture recognition

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Azriel Rosenfeld

01 Jan 1979

184 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....
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...Case(4): Suppose R = r , where r is a regular expression....
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...Equation (2) implies ri = H i Oir0 (4)...
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...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 Article•DOI•

Picture languages with array rewriting rules

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Gift Siromoney¹, Rani Siromoney¹, Kamala Krithivasan¹•Institutions (1)

Madras Christian College¹

01 Jun 1973-Information & Computation

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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139 citations