Quantitative Verification of Weighted Kripke Structures

Abstract

Abstract. Extending formal verification techniques to handle quantitative aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.

Averaging in LTL

“…The rest of the paper presents the main ideas of the proof. Due to lack of space, the full proofs could not be included here, but can be found in the research report [11] associated to this paper.…”

“…The condition imposed on p is a sufficient condition for "detecting" invalid consecutions along finite runs. The computation leading to this value is explained in the long version [11] of this work. We sketch the proof of this lemma, since it contains an interesting argument.…”

“…Such a robust undecidability is rather surprising (at least to us), given the positive results of [2] for a discounted semantics for LTL, of [22] for an extension of LTL with mean-payoff constraints. Despite the undecidability result for frequency-LTL (a boolean extension of LTL with frequency-constrained "until" modality) and for LTL with average assertions over weighted Kripke structures [8,10], we had hope that some variants of our problem would be decidable.…”