Geodesic
A symbolic method to compute the probability distribution of the number of pattern occurences in random texts generated by stochastic 0L-systems
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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The analysis of pattern occurrences has numerous applications, in particular in biology. In this article, a symbolic method is proposed to compute the distribution associated to the number of occurences of a specific pattern in a random text generated by a stochastic 0L-system. To that purpose, a semiring structure is set for combinatorial classes composed of weighted words. This algebraic structure relies on new union and concatenation operators which, under some assumptions, are admissible constructions. Decomposing the combinatorial classes of interest by using these binary operators enables the direct translation of specifications into a set of functional equations relating generating functions thanks to transformation rules. The article ends with two examples. The first one deals with unary patterns and the connection with multitype branching process is established. The second one is about a pattern composed of two letters and underlines the importance of writing a proper specification. 
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     author = {Loi, Cedric and Courn\`ede, Paul-Henry and Fran\c{c}on, Jean},
     title = {A symbolic method to compute the probability distribution of the number of pattern occurences in random texts generated by stochastic {0L-systems}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
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Loi, Cedric; Cournède, Paul-Henry; Françon, Jean. A symbolic method to compute the probability distribution of the number of pattern occurences in random texts generated by stochastic 0L-systems. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2774. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2774/

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