Distance desert automata and the star height problem
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 3, pp. 455-509.

We introduce the notion of nested distance desert automata as a joint generalization of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 2 2 𝒪(n) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration), which is the first ever complexity bound for the star height problem.

DOI : 10.1051/ita:2005027
Classification : 20M35, 68Q17, 68Q70
Mots clés : recognizable languages, star height, distance automata
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Kirsten, Daniel. Distance desert automata and the star height problem. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 3, pp. 455-509. doi : 10.1051/ita:2005027. http://archive.numdam.org/articles/10.1051/ita:2005027/

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