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Teor. Veroyatnost. i Primenen., 2002, Volume 47, Issue 4, Pages 794–803 (Mi tvp3785)  

Short Communications

Random context-free grammars: supercritical case with a nonzero extinction probability

A. I. Petrov

M. V. Lomonosov Moscow State University

Abstract: Random grammars were introduced in information science; however, investigating them with the help of methods of statistical physics, such as investigation of the thermodynamic limit, methods of cluster expansions, etc., started recently; see V. A. Malyshev [Russian Math. Surveys, 53 (1998), pp. 345–370]. For context-free grammars in a supercritical case with zero extinction probability (where symbols do not die) in [F. I. Karpelevich, V. A. Malyshev, A. I. Petrov, S. A. Pirogov, and A. N. Rybko, Context Free Evolution of Words, Rapport de Recherche No. 4413, INRIA, Rocquencourt, France, 2002] the large time behavior was studied, the existence of different limit measures was proved, and the connection between them was considered. In this paper we expand the main results of Karpelevich et al. to the supercritical case with nonzero extinction probability.

Keywords: random context-free grammar, branching process, supercritical domain, thermodynamic limit.

DOI: https://doi.org/10.4213/tvp3785

Full text: PDF file (892 kB)

English version:
Theory of Probability and its Applications, 2003, 47:4, 709–718

Bibliographic databases:

Received: 19.02.2002

Citation: A. I. Petrov, “Random context-free grammars: supercritical case with a nonzero extinction probability”, Teor. Veroyatnost. i Primenen., 47:4 (2002), 794–803; Theory Probab. Appl., 47:4 (2003), 709–718

Citation in format AMSBIB
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