The star height of reset-free events and strictly locally testable events

An algorithm is presented for determining the star height of reset-free events and strictly locally testable events

Algorithms for determining relative star height and star height

AbstractLet C = {R1, …, Rm} be a finite class of regular languages over a finite alphabet Σ. Let Δ = {b1, …, bm} be an alphabet, and δ be the substitution from Δ∗ into Σ∗ such that δ(bi) = Ri for all i (1 ≤ i ≤ m). Let R be a regular language over Σ which can be defined from C by a finite number of applications of the operators union, concatenation, and star. Then there exist regular languages over Δ which can be transformed onto R by δ. The relative star height of R w.r.t. C is the minimum star height of regular languages over Δ which can be transformed onto R by δ. This paper proves the existence of an algorithm for determining relative star height. This result obviously implies the existence of an algorithm for determining the star height of any regular language

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