ON PATTERN OCCURRENCES IN A RANDOM TEXTApril
نویسندگان
چکیده
Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have diierent probabilities of occurrence (i.e., the so called asymmetric Bernoulli model). We are concerned with the probability of exactly r occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it behaves as n r n?r?1 H , where is an explicitly computed constant, and H < 1 is the root of an equation depending on the structure of the pattern. We then extend these ndings to random patterns.
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On Pattern Occurrences in a Random Text
Consider a given pattern H and a random text T of length n. We assume that symbols in the text occur independently, and various symbols have different probabilities of occurrence (l.e., the so called asymmetric Bernoulli modeQ. We are concerned with the probability of exactly T occurrences of H in the text T. We derive the generating function of this probability, and show that asymptotically it...
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