Abstract
We show that it is undecidable whether or not two finite substitutions are equivalent on the fixed regular language ab*c. This gives an unexpected answer to a question proposed in 1985 by Culik II and Karhumäki. At the same time it can be seen as the final result in a series of undecidability results for finite transducers initiated in 1968 by Griffiths. An application to systems of equations over finite languages is given.
Research was supported by the grant 44087 of the Academy of Finland
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Karhumäki, J., Lisovik, L.P. (2002). The Equivalence Problem of Finite Substitutions on ab*c, with Applications. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_69
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DOI: https://doi.org/10.1007/3-540-45465-9_69
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