It cannot be decided whether a pushdown automaton accepts using constant pushdown height, with respect to the input length, or not. Furthermore, in the case of acceptance in constant height, the height cannot be bounded by any recursive function in the size of the description of the machine. In contrast, in the restricted case of pushdown automata over a one-letter input alphabet, i.e., unary pushdown automata, the above property becomes decidable. Moreover, if the height is bounded by a constant in the input length, then it is at most exponential with respect to the size of the description of the pushdown automaton. This bound cannot be reduced. Finally, if a unary pushdown automaton uses nonconstant height to accept, then the height should grow at least as the logarithm of the input length. This bound is optimal.
|Titolo:||Pushdown Automata and Constant Height: Decidability and Bounds|
PRIGIONIERO, LUCA (Corresponding)
|Settore Scientifico Disciplinare:||Settore INF/01 - Informatica|
|Data di pubblicazione:||2019|
|Digital Object Identifier (DOI):||10.1007/978-3-030-23247-4_20|
|Tipologia:||Book Part (author)|
|Appare nelle tipologie:||03 - Contributo in volume|