Decision Questions Concerning Semilinearity, Morphisms, and Commutation of Languages [chapter]

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2001 Lecture Notes in Computer Science  
Let be a class of automata (in a precise sense to be defined) and be the class obtained by augmenting each automaton in with finitely many reversal-bounded counters. We show that if the languages defined by are effectively semilinear, then so are the languages defined by , 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
more » ... decidability result for commutation of languages: given a fixed two element code Ã, it is undecidable whether a given context-free language Ä commutes with Ã, i.e., ÄÃ ÃÄ.
doi:10.1007/3-540-48224-5_48 fatcat:gvlbyixy75exfj72xib7zzybly