Stefan Göller

On the Computational Complexity of Verifying One-Counter Processes

One-counter processes are pushdown systems over a singleton stack alphabet (plus a stack-bottom symbol). We study the complexity of two closely related verification problems over one-counter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, and weak bisimilarity checking against finite systems. We show that both problems are

Model checking succinct and parametric one-counter automata

\P^\NP

Equivalence of deterministic one-counter automata is NL-complete

-complete. This is achieved by establishing a close correspondence with the membership problem for a natural fragment of Presburger Arithmetic, which we show to be

Bisimilarity of one-counter processes is PSPACE-complete

\P^\NP

Reachability in Two-Dimensional Vector Addition Systems with States Is PSPACE-Complete

-complete. This fragment is also a suitable representation for the global versions of the problems. We also show that there already exists a fixed EF formula(resp. a fixed finite system) such that model checking (resp. weak bisimulation) over one-counter processes is hard for

Language equivalence of deterministic real-time one-counter automata is NL-complete

\P^{\NP[\log]}

Infinite state model-checking of propositional dynamic logics

. However, the complexity drops to

Reachability in Register Machines with Polynomial Updates

\P

Bisimilarity of Pushdown Automata is Nonelementary

if the one-counter process is fixed.

Branching-Time model checking of parametric one-counter automata

We investigate the decidability and complexity of various model checking problems over one-counter automata. More specifically, we consider succinct one-counter automata, in which additive updates are encoded in binary, as well as parametric one-counter automata, in which additive updates may be given as unspecified parameters. We fully determine the complexity of model checking these automata against CTL, LTL, and modal µ-calculus specifications.