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On the decidability of some problems concerning morphisms, regular sets, and post correspondence problem

100%

Turakainen P.

tom Vol. 38, Nr 1,2

209-221

Regular languages are divided into equivalence classes according to the lengths of the words and both the universal and the existential equivalence of rational transductions on the set of these classes is studied. It is shown that the cardinality equivalence problem is undecidable for e-free finite substitutions. The morphic replication equivalence problem is arithmetized and an application to word equations is presented. Finally, the generalized Post correspondence problem is modified by using a single inverse morphism or a single finite substitution or its inverse instead of two morphisms.

Nondeterministic Bimachines and Rational Relations with Finite Codomain

100%

Santean N. , Yu S.

2006

tom Vol. 73, nr 1-2

237-264

Bimachines are important conceptual tools used for the characterization of rational word functions (realized by single-valued transducers). Despite the attention received in the past, these sequential machines are far from being exhaustively studied. A natural question which has not been addressed so far is what family of transductions are realized by bimachines that operate nondeterministically. We show that these machines characterize input-unambiguous (IU) rational transductions, i.e., those transductions that can be written as a composition of rational functions and finite substitutions. Two more families of rational transductions are defined and related in a natural way to IU transductions: input-deterministic transductions and rational transductions with finite codomain (FC). We have shown that FC transductions are recognizable and that they can be expressed as finite union of subsequential functions. Moreover, they can be realized by nondeterministic bimachines. Finally, we have defined the so called restricted nondeterministic bimachines and shown that, surprisingly, they are more powerful than nondeterministic bimachines: they characterize exactly the family of finitely ambiguous rational transductions.