Abstract It cannot be decided whether a pushdown automaton accepts using height, which does not depend on the input length, i.e., when it constant height. Furthermore, in height can arbitrarily large with respect to size of description machine, namely exist any recursive function machine bounding pushdown. In contrast, restricted case automata over one-letter alphabet, unary automata, situation...

In this paper we investigate the structure of most general kind substitution shifts, including non-minimal ones and allowing erasing morphisms. We prove decidability all properties these morphisms with respect to shift space generated by iteration, such as aperiodicity, recognizability, irreducibility or minimality.