Closure properties and complexity of rational sets of regular languages

This work received funding in part by the National Research Network RiSE on Rigorous Systems Engineering (Austrian Science Fund (FWF): S11403-N23), by the Vienna Science and Technology Fund (WWTF) through grant PROSEED, by an Erwin Schrödinger Fellowship (Austrian Science Fund (FWF): J3696-N26), and by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement DIADEM no. 246858

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