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Stochastic Methods for Generative Systems Analysis

  • Gabriel V. Orman
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A very important part in the process of transmission of information is that of generation of the words. For some time past we tried to consider the process of generation of the words by generative systems, from a stochastic point of view involving Markov chains. Because the sequences of intermediate word (called derivations) by which a word can be generated are finite, it results that finite Markov chains will be connected to the process. In order to our discussion should be as general as possible we consider generative systems free of any restrictions. The model of such systems is offered by the most general class of formal grammars from the so-called Chomsky hierarchy, namely the phrase-structure grammars. The novelty that we have proposed consists in a new organization of the process of generation of the words by considering the set of all the derivations split into equivalence classes, each of them containing derivations of the same length. In this way our results are available up to an equivalence.

Keywords

generative systems Markov chains transition matrix 

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References

  1. Ginsburg, S. (1975), Algebraic and Automata-Theoretic Properties of Formal Languages, North Holland Pub. Co., Amsterdam.Google Scholar
  2. Orman, G.V., (1982), Limbaje formale (Formal languages), Ed. Tehnica, Bucharest.Google Scholar
  3. Orman, G.V., (1993), On some numerical functions utilized in the study of a class of discrete systems, J. of Systems Science, Vol 19, No. 1, pp. 28–37.Google Scholar
  4. Orman, G.V., (1994), On the Characterization of some Generative Grammars by Numerical Functions, in: Current Issues in Mathematical Linguistics, ed. by C. Martin-Vide, Elsevier Science B.V., North Holland, Amsterdam, pp. 151–160.Google Scholar
  5. Orman, G.V., (1994), Markov chains connected to the process of generation of the words by a generative systems, Yugoslav Journal of Operations Research, Vol. 4, No. 2, pp. 167–178. Orman, G.V., (1996), Random phenomena and some systems generating words, Yugoslav Journal of Operations Research, Vol. 6, No. 2, pp. 245–256.Google Scholar
  6. Orman, G.V., (1996), On the symmetry phenomenon in generative systems, Proceedings of the International Conference on Symmetry and Antisymmetry in Mathematics, Formal Languages and Computer Science, Brasov, 18-19 July 1996, ed. by G. V. Orman, University of Brasov, pp. 87–90.Google Scholar
  7. Orman, G.V., (1997), New characterizations of generative systems, to be published in: Proceedings of the 4th Balkan Conference on Operational Research, Thessaloniki Greece, October 20 - 23.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Gabriel V. Orman
    • 1
  1. 1.Department of Mathematics“Transylvania” University of BrasovBrasovRomania

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