We study the local limit distribution of sequences of random variables representing the number of occurrences of a symbol in words of length n in a regular language, generated at random according to a rational stochastic model. We present an analysis of the main local limits when the finite state automaton defining the stochastic model consists of two primitive components. Our results include an evaluation of the convergence rate, which in the various cases is of an order slightly slower than O(n−1/2).
Goldwurm, M., Lin, J., Vignati, M., Analysis of symbol statistics in bicomponent rational models, in Hofman, P., Skrzypczak, M. (ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, Heidelberg 2019: <<LECTURE NOTES IN COMPUTER SCIENCE>>, 11647 306- 318. 10.1007/978-3-030-24886-4_23 [http://hdl.handle.net/10807/178242]
Analysis of symbol statistics in bicomponent rational models
Lin, Jianyi;
2019
Abstract
We study the local limit distribution of sequences of random variables representing the number of occurrences of a symbol in words of length n in a regular language, generated at random according to a rational stochastic model. We present an analysis of the main local limits when the finite state automaton defining the stochastic model consists of two primitive components. Our results include an evaluation of the convergence rate, which in the various cases is of an order slightly slower than O(n−1/2).
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