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by Mireille Regnier, Wojciech Szpankowski
In IEEE Computer Society, editor, Compression and Complexity of SEQUENCES 1997
http://www.deetc.isel.ipl.pt/ftp/FicheirosSeccoes/AnaliseSinais/ccd/temp/Szpankowski_CCS97_81320253.pdf
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Abstract:
Consider a given pattern H and a random text T generated randomly according to the Bernoulli model. We study the frequency of approximate occurrences of the pattern H in a random text when overlapping copies of the approximate pattern are counted separately. We provide exact and asymptotic formul for mean, variance and probability of occurrence as well as asymptotic results including the central limit theorem and large deviations. Our approach is combinatorial: we rst construct some language expressions that characterize pattern occurrences which are translated into generating functions, and nally we use analytical methods to extract asymptotic behaviors of the pattern frequency. Applications of these results include molecular biology, source coding, synchronization, wireless communications, approximate pattern matching, games, and stock market analysis. These ndings are of particular interest to information theory (e.g., second-order properties of the relative frequency), and molecular biology problems (e.g., nding patterns with unexpected high or low frequencies, and gene recognition). 1
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