Abstract
AbstractPatterns and motifs on finite alphabets are of interest in many applied areas, such as computational molecular biology, computer science, communication theory, and reliability theory. The exact distribution theory associated with occurrences of patterns (single or compound) and motifs, in random strings of letters, is treated in this chapter. The strings are generated by a Markov source, and for the case of single patterns, they are generated by general discrete-time or continuous-time models. Here, the interest is in finding closed-form expressions for the distributions of the following quantities: (i) the waiting time until the first occurrence of a pattern (motif), (ii) the intersite distances between consecutive occurrences of such, and (iii) the count of occurrences of a pattern, or more generally, the weighted count of occurrences of a compound pattern, both within a finite time horizon. General exact distribution results are discussed. Also, a brief guide on various methodological tools used in the area is provided in the Introduction.Keywords and phrasesPatternmotifwaiting timeMarkov chainsemi-Markov process
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