Decidability of a temporal logic problem for Petri nets

Witness Runs for Counter Machines

“…Let us present a fragment of Presburger LTL introduced in [Jan90] such that the atomic formulae are either control states or atomic formulae of the form…”

“…Decidability of (existential) model-checking problem for TLF restricted to VASS is established in [Jan90] by reduction into the reachability problem for VASS. Fairness conditions on VASS can be also found in [GS92].…”

A Decidable Temporal Logic of Repeating Values

“…We have shown that satisfiability for CLTL ♦ with operators in {X, X −1 , S, U} is decidable by reduction into the verification of fairness properties in Petri nets [Jan90]. The proof is uniform for the finitary and infinitary cases and it can be extended to atomic constraints of the form x = ♦ −1 y and to any set of MSOL definable temporal operators.…”

“…, x k }), K = 2 k − 1 and each set F i contains sets of states reached by decrementing the counters in C i . Lemma 4 below states that simplicity implies decidability of the nonemptiness problem thanks to [Jan90].…”

“…The possibility to compare two values at unbounded distance requires a special class of counter automata for which finitary and infinitary nonemptiness is shown decidable. To do so, we take advantage of a deep result from [Jan90] establishing that verifying fairness properties based on the temporal operator GF ("always eventually") in Petri nets is decidable. By contrast model-checking for full LTL over Petri nets is undecidable [HR89] (see also [Esp94] with lineartime mu-calculi).…”