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

TL;DR

This paper presents methods for uniform random generation of non-deterministic automata (NFA) up to isomorphism using Monte-Carlo and Metropolis-Hastings algorithms, enabling efficient sampling of complex automata subclasses.

Contribution

It introduces practical algorithms for uniform NFA generation up to isomorphism, including subclasses, with proven polynomial-time complexity and experimental validation.

Findings

Monte-Carlo approach for NFA sampling

Metropolis-Hastings algorithm for isomorphism-invariant generation

Polynomial-time complexity for subclasses of NFAs

Abstract

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.