Pattern Occurrences in Multicomponent Models

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.

[1]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[2]  Esko Ukkonen,et al.  Approximate String Matching with q-grams and Maximal Matches , 1992, Theor. Comput. Sci..

[3]  Wojciech Szpankowski,et al.  On Pattern Occurrences in a Random Text , 1996, Inf. Process. Lett..

[4]  Diego de Falco,et al.  Frequency of symbol occurrences in bicomponent stochastic models , 2004, Theor. Comput. Sci..

[5]  Arto Salomaa,et al.  Automata-Theoretic Aspects of Formal Power Series , 1978, Texts and Monographs in Computer Science.

[6]  Philippe Flajolet,et al.  Motif statistics , 1999, Theor. Comput. Sci..

[7]  Leo J. Guibas,et al.  Maximal Prefix-Synchronized Codes , 1978 .

[8]  Diego de Falco,et al.  Frequency of Symbol Occurrences in Simple Non-primitive Stochastic Models , 2003, Developments in Language Theory.

[9]  Alberto Bertoni,et al.  On the number of occurrences of a symbol in words of regular languages , 2003, Theor. Comput. Sci..

[10]  Bernard Prum,et al.  Finding words with unexpected frequencies in deoxyribonucleic acid sequences , 1995 .

[11]  Michel Rigo,et al.  Additive Functions with Respect to Numeration Systems on Regular Languages , 2003 .

[12]  Massimiliano Goldwurm.  Probabilistic Estimation of the Number of Prefixes of a Trace , 1992, Theor. Comput. Sci..

[13]  Andrzej Tarlecki,et al.  Mathematical Foundations of Computer Science 1991 , 1991, Lecture Notes in Computer Science.

[14]  Jean Berstel,et al.  Rational series and their languages , 1988, EATCS monographs on theoretical computer science.

[15]  Philippe Flajolet,et al.  Mathematics and Computer Science Iii: "Algorithms, Trees, Combinatorics And Probabilities" , 2004 .

[16]  Jérémie Bourdon,et al.  Generalized Pattern Matching Statistics , 2002 .

[17]  Esko Ukkonen,et al.  Two Algorithms for Approximate String Matching in Static Texts , 1991, MFCS.

[18]  Leonidas J. Guibas,et al.  String Overlaps, Pattern Matching, and Nontransitive Games , 1981, J. Comb. Theory A.

[19]  M S Gelfand,et al.  Prediction of function in DNA sequence analysis. , 1995, Journal of computational biology : a journal of computational molecular cell biology.

[20]  Mireille Régnier,et al.  On Pattern Frequency Occurrences in a Markovian Sequence , 1998, Algorithmica.