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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Notes
- 1.
However, due to space constraints, all proofs in the present work are omitted.
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Goldwurm, M., Lin, J., Vignati, M. (2019). Analysis of Symbol Statistics in Bicomponent Rational Models. In: Hofman, P., Skrzypczak, M. (eds) Developments in Language Theory. DLT 2019. Lecture Notes in Computer Science(), vol 11647. Springer, Cham. https://doi.org/10.1007/978-3-030-24886-4_23
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