On Boundedness Problems for Pushdown Vector Addition Systems
Résumé
We study pushdown vector addition systems,
which are synchronized products of pushdown automata with vector
addition systems.
The question of the boundedness of the reachability set for this
model
can be refined into two decision problems that ask
if infinitely many counter values or stack configurations
are reachable, respectively.
Counter boundedness seems to be the more intricate problem.
We show decidability in exponential time
for one-dimensional systems.
The proof is via a small witness property derived
from an analysis of derivation trees of
grammar-controlled vector addition systems.