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Algorithms 2011, 4, 285-306; doi:10.3390/a4040285 OPEN ACCESS algorithms ISSN 1999-4893 /journal/algorithms Article An Algorithm to Compute the Character Access Count Distribution for Pattern Matching Algorithms Tobias Marschall and Sven Rahmann Centrum Wiskunde Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands Genome Informatics, Faculty of Medicine, University of Duisburg-Essen, Hufelandstr. 55, 45122 Essen, Germany Bioinformatics, Computer Science XI, TU Dortmund, 44221 Dortmund, Germany Authors to whom correspondence should be addressed; E-Mails: T.Marschall@cwi.nl (T.M.); Sven.Rahmann@tu-dortmund.de (S.R.); Tel./Fax: +31(0)20 592 4132 ext. 4199. Received: 14 October 2011; in revised form: 26 October 2011 / Accepted: 26 October 2011 / Published: 31 October 2011 Abstract: We propose a framework for the exact probabilistic analysis of window-based pattern matching algorithms, such as Boyer–Moore, Horspool, Backward DAWG Matching, Backward Oracle Matching, and more. In particular, we develop an algorithm that efficiently computes the distribution of a pattern matching algorithm’s running time cost (such as the number of text character accesses) for any given pattern in a random text model. Text models range from simple uniform models to higher-order Markov models or hidden Markov models (HMMs). Furthermore, we provide an algorithm to compute the exact distribution of differences in running time cost of two pattern matching algorithms. Methodologically, we use extensions of finite automata which