Distance desert automata and the star height problem

Kirsten, Daniel

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 $2^{2^{𝒪\left(n\right)}}$ 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.

Classification : 20M35, 68Q17, 68Q70
Keywords: recognizable languages, star height, distance automata

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