Pictures and Chomsky Languages in Array P System
17 Aug 2015-pp 277-289
TL;DR: The regulated evolution of this new model is capable of generating interesting pictures in its accepting mode of evolution and the relationship between the family of regulating languages of 8-directional array P system and theFamily of \(\lambda \)-free regular, context-free, context to context-sensitive languages is investigated.
Abstract: A new array P system called 8-directional array P system is defined in this paper. The regulated evolution of this new model is capable of generating interesting pictures in its accepting mode of evolution. The relationship between the family of regulating languages of 8-directional array P system and the family of \(\lambda \)-free regular, context-free, context-sensitive languages is investigated. In the case of RE, the simulation result requires \(\lambda \)-labeled rules.
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TL;DR: A parallel mode of application of the contextual array rules in the regions of an array P system is considered, which means that the number of membranes needed in the constructions of the PCAP for picture array generation is reduced in comparison with the sequential counterpart.
Abstract: Contextual array P systems generate two-dimensional picture arrays by sequential application of contextual array rules on picture arrays. Here we consider a parallel mode of application of the contextual array rules in the regions of such an array P system. We call the resulting array P system as parallel contextual array P system (PCAP) and we study the generative power of these systems. A main advantage is that the number of membranes needed in the constructions of the PCAP for picture array generation is reduced in comparison with the sequential counterpart.
4 citations
Posted Content•
TL;DR: An 8-directional array P system is one where the rewriting of an array can happen in any 8-directions, and the array rules are labelled thus resulting in a labelled 8- directionalarray P system.
Abstract: An 8-directional array P system is one where the rewriting of an array can happen in any 8-directions. The array rules of such a system are labelled thus resulting in a labelled 8-directional array P system. The labelling is not unique and the label language is obtained by recording the strings over the labels used in any terminating derivation of the P system. The system is shown to generate interesting pictures. The label language is compared with Chomsky hierarchy.
Cites background from "Pictures and Chomsky Languages in A..."
...[10] An 8-directional Array P System (8dAPS) of degree m(≥ 1) is a construct...
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...[10] An 8-directional array grammar is defined to be a quadruple G = (N, T, P, S), where...
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References
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Book•
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
"Pictures and Chomsky Languages in A..." refers methods in this paper
...We construct a L8dAPS Π ′ = ( V, T, [1]1, I1, R1, 1,H, F ) , where V = {q0, q1, ....
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...Π5 = ( Q ′ ∪ {x}, {x}, [1]1, I1, R1, 1,Σ, F ) , where...
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...This computing model now has several variants [1]....
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TL;DR: It is proved that the P systems with context-free rules are computationally universal, able to generate all computable array languages.
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.
84 citations
"Pictures and Chomsky Languages in A..." refers background in this paper
...The L8dAPS Π1 with three membranes is given as, Π1 = ({ A,B,C,D, x } , { x } , [1[2]2[3]3]1, I1, I2, I3, R1, R2, R3, 3, { a } , F ) ,...
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...In [3] the authors set a collection of pictures made up of symbols to evolve using array rules mostly of isotonic type....
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...The authors in this paper also introduce a new type of isotonic rule called restricted monotonic type which is different from the array rules used in [3]....
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01 Apr 1970
TL;DR: This paper focuses on isotonic context-sensitive array rewriting rules, which are essentially the same as local digital picture processing operations and are of interest to study (string) grammars which operate in parallel.
Abstract: : When one attempts to generalize phrase-structure grammars from strings to arrays, difficulties arise which can be avoided if the grammars are required to be isotonic: in any array rewriting rule, the left and right members are congruent subarrays. Isotonic context-sensitive array rewriting rules are essentially the same as local digital picture processing operations. Since the latter are often applied to pictures in parallel, it is of interest to study (string) grammars which operate in parallel: that is, when a rule is applied to a string, every instance of the left member is replaced by the right member. (Here again, there are difficulties which can be avoided if all rules are isotonic and context-sensitive.) The sets of sentences which such a parallel grammar generates is not the same as the set of sentences which it parses, nor is either of these the same as the set of sentences generated (or parsed) when rules need not be applied in parallel. However, any parallel language is a sequential language and vice versa. (Author)
64 citations
"Pictures and Chomsky Languages in A..." refers background in this paper
...In [5] the authors looked at the regulating evolution of an isotonic array P system where the evolution rules were either regular isotonic or context-free isotonic as defined in [6]....
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Proceedings Article•
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02 Dec 1986
TL;DR: This tutorial briefly introduces array grammars, in which rewriting rules involve replacement of subarrays bySubarrays, and the extension to arbitrary dimensions is straightforward.
20 citations
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.
16 citations