Pattern Occurrences in Multicomponent Models

Goldwurm, Massimiliano; Lonati, Violetta

doi:10.1007/978-3-540-31856-9_56

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…This goal is also partly related to the Schur and Frobenius problems, nice unimodality/logconcavity questions, and knapsack-like problems or even polytope volume computations, where one is interested in counting the number of nonnegative integer solutions to equations like a i x i = n, for some fixed integers a i . Going back to the language theoretic perspective, in an important sequence of articles [1,3,18,9], Goldwurm, Lonati, Choffrut & Bertoni have studied the distribution of occurrences of a given pattern in the language of a regular expression. They identified an important influence of the number of strongly connected components in the transition matrix, and of their relative intrication.…”

Section: Introductionmentioning

confidence: 99%

On the diversity of pattern distributions in rational language.

Banderier¹,

Bodini²,

Ponty³

et al. 2012

2012 Proceedings of the Ninth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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It is well known that, under some aperiodicity and irreducibility conditions, the number of occurrences of local patterns within a Markov chain (and, more generally, within the languages generated by weighted regular expressions/automata) follows a Gaussian distribution with both variance and mean in Θ(n). By contrast, when these conditions no longer hold, it has been observed that the limiting distribution may follow a whole diversity of distributions, including the uniform, powerlaw or even multimodal distribution, arising as tradeoffs between structural properties of the regular expression and the weight/probabilities associated with its transitions/letters. However these cases only partially cover the full diversity of behaviors induced within regular expressions, and a characterization of attainable distributions remained to be provided.In this article, we constructively show that the limiting distribution of the simplest foreseeable motif (a single letter!) may already follow an arbitrarily complex continuous distribution (or cadlag process). We also give applications in random generation (Boltzmann sampling) and bioinformatics (parsimonious segmentation of DNA).

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Section: Introductionmentioning

confidence: 99%

On the diversity of pattern distributions in rational language.

Banderier¹,

Bodini²,

Ponty³

et al. 2012

2012 Proceedings of the Ninth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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“…The same property can be proved for the number of occurrences of a given symbol in words generated by primitive rational models and, more generally, by rational models having a unique dominant component, that is a primitive component with a maximum eigenvalue. In [4,8] more general conditions are given that guarantee a Gaussian limit distribution for the same quantity in rational models. Here, we want to give a further analogy between Markov chains and rational models concerning the fundamental matrix Z given in Section 1.…”

Section: Fundamental Matrix In Primitive Rational Modelsmentioning

confidence: 99%

Probabilistic models for pattern statistics

Goldwurm

Radicioni

2006

RAIRO-Theor. Inf. Appl.

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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.

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