On the asymptotic enumeration of accessible automata

Lebensztayn, Élcio

doi:10.46298/dmtcs.512

Cited by 4 publications

(2 citation statements)

References 5 publications

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“…Carayol and Nicaud derived a simple and explicit formula of this constant from their theorem. (The same formula is also proved by Lebensztayn [29] with a more analytic approach using Lagrange series. )…”

Section: The Model and The Historysupporting

confidence: 61%

The graph structure of a deterministic automaton chosen at random

Cai

Devroye

2016

Random Struct Algorithms

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An n‐state deterministic finite automaton over a k‐letter alphabet can be seen as a digraph with n vertices which all have k labeled out‐arcs. Grusho (Publ Math Inst Hungarian Acad Sci 5 (1960), 17–61). proved that whp in a random k‐out digraph there is a strongly connected component of linear size, i.e., a giant, and derived a central limit theorem. We show that whp the part outside the giant contains at most a few short cycles and mostly consists of tree‐like structures, and present a new proof of Grusho's theorem. Among other things, we pinpoint the phase transition for strong connectivity. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 428–458, 2017

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Section: The Model and The Historysupporting

confidence: 61%

The graph structure of a deterministic automaton chosen at random

Cai

Devroye

2016

Random Struct Algorithms

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“…This asymptotic estimate for |A n | was originally established by Korshunov [14], and reformulated in terms of the Stirling numbers in [1, Theorem 18]. The simplified expression for the constant κ (which is denoted in [1] by E 2 ) is due to Lebensztayn [15].…”

Section: Auxiliary Resultsmentioning

confidence: 98%

A large deviations principle for the Maki–Thompson rumour model

Lebensztayn

2015

Journal of Mathematical Analysis and Applications

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We consider the stochastic model for the propagation of a rumour within a population which was formulated by Maki and Thompson [20]. Sudbury [22] established that, as the population size tends to infinity, the proportion of the population never hearing the rumour converges in probability to 0.2032. Watson [23] later derived the asymptotic normality of a suitably scaled version of this proportion. We prove a corresponding large deviations principle, with an explicit formula for the rate function.

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Random Deterministic Automata

Nicaud¹

2014

Mathematical Foundations of Computer Science 2014

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Abstract. In this article, we consider deterministic automata under the paradigm of average case analysis of algorithms. We present the main results obtained in the literature using this point of view, from the very beginning with Korshunov's theorem about the asymptotic number of accessible automata to the most recent advances, such as the average running time of Moore's state minimization algorithm or the estimation of the probability that an automaton is minimal. While focusing on results, we also try to give an idea of the main tools used in this field.

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On the asymptotic enumeration of accessible automata

Cited by 4 publications

References 5 publications

The graph structure of a deterministic automaton chosen at random

The graph structure of a deterministic automaton chosen at random

A large deviations principle for the Maki–Thompson rumour model

Random Deterministic Automata

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