Automata and rational expressions

This text is an extended version of the chapter 'Automata and rational expressions' in the AutoMathA Handbook that will appear soon, published by the European Science Foundation and edited by JeanEricPin

Distance Desert Automata and Star Height Substitutions

We introduce the notion of nested distance desert automata as a joint generalization and further development 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 22O(n2) 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). We also show some decidability results for some substitution problems for recognizable languages

On the star height of rational languages: a new presentation for two old results

International audienc

On the star height of rational languages: a new presentation for two old results

International audienc