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Undecidability of the equivalence of finite substitutions on regular language

Published online by Cambridge University Press:  15 August 2002

Vesa Halava  and
Tero Harju
Vesa Halava
Affiliation:
Turku Centre for Computer Science TUCS, Lemminkäisenkatu 14 A, FIN-20520 Turku, Finland; vehalava@cs.utu.fi.
Tero Harju
Affiliation:
Department of Mathematics, University of Turku, FIN-20014 Turku, Finland; harju@utu.fi.
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Abstract

A simplified proof is given for the following result due to Lisovik: it is undecidable for two given ε–free finite substitutions, whether they are equivalent on the regular language b{0,1}*c.

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 2 , March 1999 , pp. 117 - 124
Copyright
© EDP Sciences, 1999

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References

V. Halava and T. Harju, Undecidability in integer weighted finite automata. Fund. Inform., to appear.
Karhumäki, J., Equations over finite sets of words and equivalence problems in automata theory. Theoret. Comput. Sci. 108 (1993) 103-118. CrossRef
Lisovik, L.P., An undecidable problem for countable Markov chains. Cybernetics 27 (1991) 163-169. CrossRef
L.P. Lisovik, Nondeterministic systems and finite substitutions on regular language. Bull. European Assoc. Theoret. Comput. Sci. (1997) 156-160.
Turakainen, P., The undecidability of some equivalence problems concerning ngsm's and finite substitutions. Theoret. Comput. Sci. 174 (1997) 269-274. CrossRef