An Automata-based Approach for CTL*; With Constraints
Electronic Notes in Theoretical Computer Science (ENTCS)
Reachability in Succinct and Parametric One-Counter Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Model checking memoryful linear-time logics over one-counter automata
Theoretical Computer Science
Completeness of the bounded satisfiability problem for constraint LTL
RP'11 Proceedings of the 5th international conference on Reachability problems
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We study decidability and complexity issues for fragments of LTL with Presburger constraints by restricting the syntactic resources of the formulae (the class of constraints, the number of variables and the distance between two states for which counters can be compared) while preserving the strength of the logical operators. We provide a complete picture refining known results from the literature, in some cases pushing forward the known decidability limits. By way of example, we show that model-checking formulae from LTL with quantifier-free Presburger arithmetic over one-counter automata is only PSPACE-complete. In order to establish the PSPACE upper bound, we show that the nonemptiness problem for Buchi one-counter automata taking values in \mathbb{Z} and allowing zero tests and sign tests, is only NLOGSPACE-complete.