In this work we study some probabilistic models for the random generation of words over a given alphabet used in the literature in connection with pattern statistics. Our goal is to compare models based on markovian processes (where the occurrence of a symbol in a given position only depends on a finite number of previous occurrences) and the stochastic models that can generate a word of given length from a regular language under uniform distribution. We present some results that show the differences between these two stochastic models and their relationship with the rational probabilistic measures.
Keywords: pattern statistics, Markov chains, probabilistic automata, rational formal series
@article{ITA_2006__40_2_207_0, author = {Goldwurm, Massimiliano and Radicioni, Roberto}, title = {Probabilistic models for pattern statistics}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {207--225}, publisher = {EDP-Sciences}, volume = {40}, number = {2}, year = {2006}, doi = {10.1051/ita:2006003}, mrnumber = {2252636}, zbl = {1112.68086}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2006003/} }
TY - JOUR AU - Goldwurm, Massimiliano AU - Radicioni, Roberto TI - Probabilistic models for pattern statistics JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 SP - 207 EP - 225 VL - 40 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2006003/ DO - 10.1051/ita:2006003 LA - en ID - ITA_2006__40_2_207_0 ER -
%0 Journal Article %A Goldwurm, Massimiliano %A Radicioni, Roberto %T Probabilistic models for pattern statistics %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2006 %P 207-225 %V 40 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2006003/ %R 10.1051/ita:2006003 %G en %F ITA_2006__40_2_207_0
Goldwurm, Massimiliano; Radicioni, Roberto. Probabilistic models for pattern statistics. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 2, pp. 207-225. doi : 10.1051/ita:2006003. http://www.numdam.org/articles/10.1051/ita:2006003/
[1] Modules over a ring of differential operators, study of the fundamental solutions of equations with constant coefficients. Functional Anal. Appl. 5 (1971) 1-16 (Russian); pages 89-101 (English). | Zbl
,[2] Rational Series and their Languages. Springer-Verlag, New York, Heidelberg, Berlin (1988). | MR | Zbl
and ,[3] On the number of occurrences of a symbol in words of regular languages. Theoret. Comput. Sci. 302 (2003) 431-456. | Zbl
, , and ,[4] Local limit properties for pattern statistics and rational models. Theory. Comput. Syst. 39 (2006) 209-235. | Zbl
, , and ,[5] Generalized pattern matching statistics. Mathematics and computer science II: algorithms, trees, combinatorics and probabilities, in Proc. of Versailles Colloquium. Birkhauser (2002) 249-265 | Zbl
and ,[6] Génération aléatoire et uniforme de mots de langages rationnels. Theoret. Comput. Sci. 159 (1996) 43-63. | Zbl
,[7] A calculus for the random generation of labelled combinatorial structures. Theoret. Comput. Sci. 132 (1994) 1-35. | Zbl
, and ,[8] Pattern occurrences in multicomponent models, in Proc. 22nd STACS. Lect. Notes Comput. Sci. 3404 (2005) 680-692. | Zbl
and ,[9] Rational probability measures. Theoret. Comput. Sci. 65 (1989) 171-188 (french version in Mots, edited by M. Lothaire, Hermes (1990) 335-357). | Zbl
and ,[10] Finite Markov Processes and Their Applications. J. Wiley and Son (1980). | MR | Zbl
,[11] Analytic approach to pattern matching, Chap. 7 in Applied Combinatorics on Words. Cambridge University Press (2005).
and ,[12] Finite Markov Chains. Van Nostrand (1960). | MR | Zbl
and ,[13] -finite power series. J. Algebra 122 (1989) 353-373. | Zbl
,[14] Motif statistics. Theoret. Comput. Sci. 287 (2002) 593-617. | Zbl
, and ,[15] Introduction to Probabilistic Automata. Academic Press (1971). | MR | Zbl
,[16] On pattern frequency occurrences in a Markovian sequence. Algorithmica 22 (1998) 621-649. | Zbl
and ,[17] Automata-Theoretic Aspects of Formal Power Series. Springer-Verlag (1978). | MR | Zbl
and ,[18] Non-negative Matrices and Markov Chains. Springer-Verlag (1981). | MR | Zbl
,[19] Differentiably finite power series. Eur. J. Combin. 1 (1980) 175-188. | Zbl
,Cited by Sources: