Desert automata and the finite substitution problem

Abstract

We give a positive solution to the so-called finite substitution problem which was open for more than 10 years [11]: given recognizable languages K and L, decide whether there exists a finite substitution σ such that σ(K) = L. For this, we introduce a new model of weighted automata and show the decidability of its limitedness problem by solving the underlying Burnside problem. © Springer-Verlag 2004.