Abstract
In this paper we determine some limit distributions of pattern statistics in rational stochastic models, defined by means of nondeterministic weighted finite automata. We present a general approach to analyse these statistics in rational models having an arbitrary number of connected components. We explicitly establish the limit distributions in the most significant cases; these ones are characterized by a family of unimodal density functions defined by polynomials over adjacent intervals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstel, J., Reutenauer, C.: Rational series and their languages. Springer, Heidelberg (1988)
Bertoni, A., Choffrut, C., Goldwurm, M., Lonati, V.: On the number of occurrences of a symbol in words of regular languages. Theoret. Comput. Sci. 302(1-3), 431–456 (2003)
Bourdon, J., Vallée, B.: Generalized pattern matching statistics. In: Mathematics and computer science II: algorithms, trees, combinatorics and probabilities. Proc. of Versailles Colloquium, pp. 249–265. Birkhäuser, Basel (2002)
de Falco, D., Goldwurm, M., Lonati, V.: Frequency of symbol occurrences in bicomponent stochastic models. Theoret. Comput. Sci. 327(3), 269–300 (2004)
Fudos, I., Pitoura, E., Szpankowski, W.: On pattern occurrences in a random text. Inform. Process. Lett. 57, 307–312 (1996)
Gelfand, M.S.: Prediction of function in DNA sequence analysis. J. Comput. Biol. 2, 87–117 (1995)
Gnedenko, B.V.: The theory of probability (translated by Yankovsky, G.). Mir Publishers, Moscow (1976)
Goldwurm, M.: Probabilistic estimation of the number of prefixes of a trace. Theoret. Comp. Sci. 92, 249–268 (1992)
Grabner, P., Rigo, M.: Additive functions with respect to numeration systems on regular languages. Monatshefte für Mathematik 139, 205–219 (2003)
Guibas, L.J., Odlyzko, A.M.: Maximal prefix-synchronized codes. SIAM J. Appl. Math. 35, 401–418 (1978)
Guibas, L.J., Odlyzko, A.M.: String overlaps, pattern matching, and nontransitive games. Journal of Combinatorial Theory. Series A 30(2), 183–208 (1981)
Jokinen, P., Ukkonen, E.: Two algorithms for approximate string matching in static texts. In: Tarlecki, A. (ed.) MFCS 1991. LNCS, vol. 520, p. 248. Springer, Heidelberg (1991)
Nicodeme, P., Salvy, B., Flajolet, P.: Motif statistics. Theoret. Comput. Sci. 287(2), 593–617 (2002)
Prum, B., Rudolphe, F., Turckheim, E.: Finding words with unexpected frequencies in deoxyribonucleic acid sequence. J. Roy. Statist. Soc. Ser. B 57, 205–220 (1995)
Régnier, M., Szpankowski, W.: On pattern frequency occurrences in a Markovian sequence. Algorithmica 22(4), 621–649 (1998)
Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Springer, Heidelberg (1978)
Seneta, E.: Non-negative matrices and Markov chains. Springer, Heidelberg (1981)
Ukkonen, E.: Approximate string-matching with q-grams and maximal matchings. Theoret. Comput. Sci. 92, 191–211 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goldwurm, M., Lonati, V. (2005). Pattern Occurrences in Multicomponent Models. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_56
Download citation
DOI: https://doi.org/10.1007/978-3-540-31856-9_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24998-6
Online ISBN: 978-3-540-31856-9
eBook Packages: Computer ScienceComputer Science (R0)