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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 adoi:10.1006/jcss.2002.1836 fatcat:jbmvukk7o5d67dhmzhza3u47gi