On languages of automaton counter machines

A class of formal languages (ACML) acceptable by automaton counter machines is considered. This class is shown to be close with respect to the operations of union, regular intersection, concatenation, infinite iteration, homomorphism, and inverse homomorphism. It follows from here that this class is a full abstract family of languages [7] with all the properties following from this. Furthermore, the ACML is close with respect to intersection and substitution but is not closed with respect to complement and reverse. For the ACML class, the problems of emptiness and recognition of words of a language given by an automaton counter machine are decidable, but the problems of inclusion and equivalence of languages are undecidable. A comparison with other classes of languages (regular, context-free, context-sensitive, and Petri-net languages) is performed.