Some Decision Problems Concerning Semilinearity and Commutation

Tero Harju, Oscar Ibarra, Juhani Karhumäki, Arto Salomaa
2002 Journal of computer and system sciences (Print)  
Let M be a class of automata (in a precise sense to be defined) and M c the class obtained by augmenting each automaton in M with finitely many reversal-bounded counters. We show that if the languages defined by M are effectively semilinear, then so are the languages defined by M 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
more » ... rprising 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 ¼ KL. # 2002 Elsevier Science (USA)
doi:10.1006/jcss.2002.1836 fatcat:jbmvukk7o5d67dhmzhza3u47gi