The simplest language where equivalence of finite substitutions is undecidable

Authors:
Michal Kunc
Affiliations:
Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic
Venue:
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Year:
2007

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Abstract

We show that it is undecidable whether two finite substitutions agree on the binary language a*b. This in particular means that equivalence of nondeterministic finite transducers is undecidable even for two-state transducers with unary input alphabet and whose all transitions start from the initial state.