QuAK: Quantitative Automata Kit

Abstract

System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including $${\textsf{Inf}}$$ Inf , $${\textsf{Sup}}$$ Sup , $${\textsf{LimInf}}$$ LimInf , $${\textsf{LimSup}}$$ LimSup , $${\textsf{LimInfAvg}}$$ LimInfAvg , and $${\textsf{LimSupAvg}}$$ LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems.