Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages
Let ℭ be a class of automata (in a precise sense to be defined) and ℭc the class obtained by augmenting each automaton in ℭ with finitely many reversal-bounded counters. We first show that if the languages defined by ℭ are effectively semilinear, then so are the languages defined by ℭc, and, hence, their emptiness problem is decidable. This result is then used to show the decidability of various problems concerning morphisms and commutation of languages. We also prove a surprising undecidability result: given a fixed two element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK = KL.
KeywordsReversal-bounded counters context-free languages combinatorics on words commutation of languages morphisms
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