Random Generation of Deterministic Acyclic Automata Using Markov Chains

Abstract

Abstract. In this article we propose an algorithm, based on Markov chain techniques, to generate random automata that are deterministic, accessible and acyclic. The distribution of the output approaches the uniform distribution on n-state such automata. We then show how to adapt this algorithm in order to generate minimal acyclic automata with n states almost uniformly.

Random Generation of Source Vectors with a Fixed Determining Property

“…It is often very difficult to obtain the mixing time, that is the number of steps needed to get close enough to the sought distribution (often the uniform one). As a consequence, it is often difficult to obtain a tight bound on the complexity of such algorithms [18,8,12]. This paper presents a Markov Chained based algorithm of source vectors with fixed properties.…”

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

“…In [8,9] NFAs are obtained by the random generation of a regular expression and by transforming it into an equivalent automaton using Glushkov Algorithm. The use of Markov chains based techniques to randomly generate finite automata was introduced in [10,11] for acyclic automata.…”

Random Generation and Enumeration of Accessible Deterministic Real-Time Pushdown Automata

“…The random generation of possibly incomplete automata is analyzed in [BDN09]. The recent paper [CF11] presents how to use Monte-Carlo approaches to generate deterministic acyclic automata. As far as we know, the only work focusing on the random generation of deterministic transducers is [HNS10].…”