Enumeration and random generation of accessible automata

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We present a bijection between the set An of deterministic and accessible automata with n states on a k-letters alphabet and some diagrams, which can themselves be represented as partitions of a set of k n + 1 elements into n non-empty subsets. This combinatorial construction shows that the asymptotic order of the cardinality of An is related to the Stirling number {(k n; n)}. Our bijective approach also yields an efficient random sampler, for the uniform distribution, of automata with n states, its complexity is O (n3 / 2), using the framework of Boltzmann samplers. © 2007 Elsevier Ltd. All rights reserved.




Bassino, F., & Nicaud, C. (2007). Enumeration and random generation of accessible automata. Theoretical Computer Science, 381(1–3), 86–104. https://doi.org/10.1016/j.tcs.2007.04.001

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