A new dichotomic algorithm for the uniform random generation of words in regular languages (journal version)

Johan Oudinet 1 Alain Denise 1, 2, 3 Marie-Claude Gaudel 1
2 AMIB - Algorithms and Models for Integrative Biology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France
Abstract : We present a new algorithm for generating uniformly at random words of any regular language $\mathcal{L}$. When using floating point arithmetics, its bit-complexity is $\mathcal{O}(q \log^2 n)$ in space and $\mathcal{O}(q n \log^2 n)$ in time, where $n$ stands for the length of the word, and $q$ stands for the number of states of a finite deterministic automaton of $\mathcal{L}$. We implemented the algorithm and compared its behavior to the state-of-the-art algorithms, on a set of large automata from the VLTS benchmark suite. Both theoretical and experimental results show that our algorithm offers an excellent compromise in terms of space and time requirements, compared to the known best alternatives. In particular, it is the only method that can generate long paths in large automata.
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Johan Oudinet, Alain Denise, Marie-Claude Gaudel. A new dichotomic algorithm for the uniform random generation of words in regular languages (journal version). Theoretical Computer Science, Elsevier, 2013, 502, pp.165-176. ⟨hal-00716558⟩

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