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A Burnside Approach to the Finite Substitution Problem

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Abstract

We introduce a new model of weighted automata: the desert automata. We show that their limitedness problem is PSPACE-complete by solving the underlying Burnside problem. As an application of this result, we give a positive solution to the so-called finite substitution problem which was open for more than 10 years: given recognizable languages K and L, decide whether there exists a finite substitution σ such that σ(K) = L.

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  1. Institute of Algebra, Dresden University of Technology, D-01062 Dresden, Germany

    Daniel Kirsten

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  1. Daniel Kirsten
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Correspondence to Daniel Kirsten.

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Kirsten, D. A Burnside Approach to the Finite Substitution Problem. Theory Comput Syst 39, 15–50 (2006). https://doi.org/10.1007/s00224-005-1255-x

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  • DOI: https://doi.org/10.1007/s00224-005-1255-x

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