Reasoning about reversal-bounded counter machines

International audienceIn this paper, we present a short survey on reversal-bounded counter machines. It focuses on the main techniques for model-checking such counter machines with specifications expressed with formulae from some linear-time temporal logic. All the decision procedures are designed by translation into Presburger arithmetic. We provide a proof that is alternative to Ibarra's original one for showing that reachability sets are effectively definable in Presburger arithmetic. Extensions to repeated control state reachability and to additional temporal properties are discussed in the paper. The article is written to the honor of Professor Ewa Orłowska and focuses on several topics that are developped in her works

Presburger liveness verification of discrete timed automata

Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decidable, given a discrete timed automaton A and a Presburger property P, whether there exists an ω-path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for eachω-path of A. These results might give insights into the corresponding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata