On the Uniform Random Generation of Non Deterministic Automata Up to Isomorphism

In this paper we address the problem of the uniform random generation of non deterministic automata (NFA) up to isomorphism. First, we show how to use a Monte-Carlo approach to uniformly sample a NFA. Secondly, we show how to use the Metropolis-Hastings Algorithm to uniformly generate NFAs up to isomorphism. Using labeling techniques, we show that in practice it is possible to move into the modified Markov Chain efficiently, allowing the random generation of NFAs up to isomorphism with dozens of states. This general approach is also applied to several interesting subclasses of NFAs (up to isomorphism), such as NFAs having a unique initial states and a bounded output degree. Finally, we prove that for these interesting subclasses of NFAs, moving into the Metropolis Markov chain can be done in polynomial time. Promising experimental results constitute a practical contribution.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223, pp.12, 2015, Implementation and Application of Automata - 20th International Conferenc

Sampling different kinds of acyclic automata using Markov chains

International audienceWe propose algorithms that use Markov chain techniques to generate acyclic automata uniformly at random. We first consider deterministic, accessible and acyclic automata, then focus on the class of minimal acyclic automata. In each case we explain how to define random local transformations that describe an ergodic and symmetric Markov chain; the distribution of the automaton obtained after T random steps in this Markov chain tends to the uniform distribution as T tends to infinity