Pushdown automata and constant height: decidability and bounds

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 is different. First, acceptance decidable. Moreover, at most exponential automaton. We also prove matching lower bound. Finally, if uses nonconstant accept, then should grow least as logarithm length. This bound optimal.