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Waiting time distributions for pattern occurrence in a constrained sequence

Abstract : A binary sequence of zeros and ones is called a (d; k)-sequence if it does not contain runs of zeros of length either lessthan d or greater than k, where d and k are arbitrary, but fixed, non-negative integers and d < k. Such sequences find requires that (d; k)-sequences do not contain a specific pattern w. Therefore, distribution results concerning pattern occurrence in (d; k)-sequences are of interest. In this paper we study the distribution of the waiting time until the r-th occurrence of a pattern w in a random (d; k)-sequence generated by a Markov source. Numerical examples are also provided.
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Valeri T. Stefanov, Wojciech Szpankowski. Waiting time distributions for pattern occurrence in a constrained sequence. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (1), pp.305--320. ⟨hal-00966498⟩

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