Skip to Main content Skip to Navigation
New interface
Conference papers

Accessible and Deterministic Automata: Enumeration and Boltzmann Samplers

Abstract : We present a bijection between the set $\mathcal{A}_n$ of deterministic and accessible automata with $n$ states on a $k$-letters alphabet and some diagrams, which can themselves be represented as partitions of the set $[\![ 1..(kn+1) ]\!]$ into $n$ non-empty parts. This combinatorial construction shows that the asymptotic order of the cardinality of $\mathcal{A}_n$ is related to the Stirling number $\{^{kn}_n\}$. Our bijective approach also yields an efficient random sampler of automata with $n$ states, of complexity $O(n^{3/2})$, using the framework of Boltzmann samplers.
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 2:24:29 PM
Last modification on : Wednesday, January 19, 2022 - 4:42:04 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:09:04 PM


Publisher files allowed on an open archive



Frédérique Bassino, Cyril Nicaud. Accessible and Deterministic Automata: Enumeration and Boltzmann Samplers. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.151-160, ⟨10.46298/dmtcs.3499⟩. ⟨hal-00619870v2⟩



Record views


Files downloads