Automating the Analysis of Quantitative Automata with QuAK

TL;DR

This paper introduces enhancements to QuAK, a software tool for analyzing quantitative automata, by adding features that provide witnesses for decision problems and support for nondeterministic automata, advancing automated system analysis.

Contribution

The paper extends QuAK with witness generation for inclusion and top value computations, and introduces a new safety-liveness decomposition algorithm for nondeterministic automata.

Findings

QuAK now provides witnesses for inclusion and top value results.

The new safety-liveness decomposition handles nondeterministic automata.

Enhanced QuAK improves automation and informativeness in quantitative automata analysis.

Abstract

Quantitative automata model beyond-boolean aspects of systems: every execution is mapped to a real number by incorporating weighted transitions and value functions that generalize acceptance conditions of boolean $\omega$-automata. Despite the theoretical advances in systems analysis through quantitative automata, the first comprehensive software tool for quantitative automata (Quantitative Automata Kit, or QuAK) was developed only recently. QuAK implements algorithms for solving standard decision problems, e.g., emptiness and universality, as well as constructions for safety and liveness of quantitative automata. We present the architecture of QuAK, which reflects that all of these problems reduce to either checking inclusion between two quantitative automata or computing the highest value achievable by an automaton -- its so-called top value. We improve QuAK by extending these two algorithms with an option to return, alongside their results, an ultimately periodic word witnessing the algorithm's output, as well as implementing a new safety-liveness decomposition algorithm that can handle nondeterministic automata, making QuAK more informative and capable.