9 research outputs found
Reachability in Continuous Pushdown VASS
Pushdown Vector Addition Systems with States (PVASS) consist of finitely many
control states, a pushdown stack, and a set of counters that can be incremented
and decremented, but not tested for zero. Whether the reachability problem is
decidable for PVASS is a long-standing open problem.
We consider continuous PVASS, which are PVASS with a continuous semantics.
This means, the counter values are rational numbers and whenever a vector is
added to the current counter values, this vector is first scaled with an
arbitrarily chosen rational factor between zero and one. We show that
reachability in continuous PVASS is NEXPTIME-complete. Our result is unusually
robust: Reachability can be decided in NEXPTIME even if all numbers are
specified in binary. On the other hand, NEXPTIME-hardness already holds for
coverability, in fixed dimension, for bounded stack, and even if all numbers
are specified in unary
Languages ordered by the subword order
We consider a language together with the subword relation, the cover
relation, and regular predicates. For such structures, we consider the
extension of first-order logic by threshold- and modulo-counting quantifiers.
Depending on the language, the used predicates, and the fragment of the logic,
we determine four new combinations that yield decidable theories. These results
extend earlier ones where only the language of all words without the cover
relation and fragments of first-order logic were considered