Combinatorial and Computational Problems on Finite Sets of Words
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
On the Complexity of Decidable Cases of Commutation Problem for Languages
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
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Let C be a class of automata (in a precise sense to be defined) and C c be the class obtained by augmenting each automaton in C with finitely many reversal-bounded counters. We show that if the languages defined by C are effectively semilinear, then so are the languages defined by C c , and, hence, their emptiness problem is decidable. We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages. We also prove a surprising undecidability result for commutation of languages: given a fixed two element code K , it is undecidable whether a given context-free language L commutes with K , i.e., LK = KL.