Context dependent Table matrix L systems
TL;DR: The typical hierarchy result is proved in this case and it is seen that this generates some interesting classes of pictures.
About: This article is published in Information Sciences.The article was published on 1985-09-01. It has received 3 citations till now. The article focuses on the topics: Matrix (mathematics) & Context (language use).
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TL;DR: It is observed that by introducing just one operator E the authors can make the table matrix L systems generate almost all the pictures which were previously generated by combining the lack of a completeness condition and partial coding on TMLS.
4 citations
TL;DR: The proposed Restricted Pushdown Array of Counters-Finite Matrix Automaton (RPAC-FMA) is proposed and it is shown that a lanauge is RPAC-FM Language if and only if it is a EOL-RM Language.
Abstract: In formal language theory, a traditional topic is to characterize classes of languages by machine models. Motivated by the idea of extending the machine characterization of L systems to two dimensions and at the same time to generate interesting picture classes we propose in this paper a new model called EOL-Regular Matrix Systems (EOL-RMS). EOL-RM languages are obtained by substituting regular sets vertically into EOL languages. First a horizontal line of intermediates is generated by an EOL system. Then regular sets are substituted vertically for each intermediate eel! resulting in a rectangular array. We propose in this paper Restricted Pushdown Array of Counters-Finite Matrix Automaton (RPAC-FMA) and show that a lanauge is RPAC-FM Language if and only if it is a EOL-RM Language.
2 citations
TL;DR: It is shown that a language is a (RPAC-RPAC)AA language if and only if it is a E0L-E0L language, which is a two-dimensional language which need not be rectangular.
1 citations
References
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Book•
01 Jan 1980TL;DR: A survey of the different areas of the theory of developmental systems and languages in such a way that it discusses typical results obtained in each particular problem area.
Abstract: The paper gives a survey of the different areas of the theory of developmental systems and languages. It is organized in such a way that it discusses typical results obtained in each particular problem area. The results quoted may not always be the most important ones but they are quite representative for the direction of research in this theory. Proofs are not given and, consequently, the basic techniques for solving problems in this theory are not discussed. An attempt has been made to cover also the most recent results. Most of the results have not yet appeared in print. To appear in J. Tou (ed. ), Advances in Information Systems Science, Plenum Press.
771 citations
Book•
01 Jan 1975
TL;DR: Developmental systems were introduced in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms by considering the states and outputs to be identical and thus omitting the output functions.
Abstract: Developmental systems were introduced (Lindenmayer, 1968, 1971) in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms. These systems were originally conceived as linear arrays of interconnected finite automata, each automaton corresponding to a living cell, with the possibility that new automata can be added to the array (cells divide) or be deleted from the array (cells die). Each cell in the array is supposed to have the same state-transition and output functions. As required by biological considerations these functions must be applied to all cells in the array simultaneously at each time step. Thus one obtains infinite sequences of arrays once the functions and the initial arrays are specified. Simplified constructs are defined (and used in this paper) by considering the states and outputs to be identical and thus omitting the output functions. Such filamentous developmental systems have been called “Lindenmayer models” Herman, 1969, 1970) or “L-systems” (Van Dalen, 1971).
423 citations
TL;DR: A linguistic model to generate matrices (arrays of terminals) is presented and immediate application is shown in picture processing by generating a wide class of interesting pictures.
167 citations
"Context dependent Table matrix L sy..." refers background in this paper
...For the definitions of the above operations, the reader is referred to [7]....
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TL;DR: The notions of matrix and vector control are introduced, and the effects of these mechanisms are investigated, which leads to results very much different from corresponding well-known results for context-free grammars.
Abstract: This paper is concerned with extended OL systems and the effects (with respect to the generative capacity) on these systems caused by and their combinations. Among other things it is proven that the effect of 3) is strictly stronger than the effect of both 1) and 2), and equal to the effect of the combination of 1) and 2). This implies among other things that the effect of appearance checking on the systems with regular control is significant.
Finally the notions of matrix and vector control are introduced, and the effects of these mechanisms are investigated. This leads to results very much different from corresponding well-known results for context-free grammars.
20 citations