Automating the Analysis of Quantitative Automata with QuAK

2025-01-27

AI Summary

This paper addresses fundamental challenges in quantitative automata analysis—including emptiness/universality checking, language inclusion, supremum computation, and safety-liveness decomposition—by introducing QuAK, the first open-source tool for quantitative automata analysis. Methodologically, QuAK (1) introduces the first inclusion and supremum algorithms that construct ultimately periodic witness words; (2) proposes a novel safety-liveness decomposition technique tailored to nondeterministic weighted ω-automata; and (3) unifies diverse verification tasks as reductions to inclusion checking and supremum optimization, integrating weighted automata theory, ω-regular semantics modeling, and symbolic construction techniques. Implemented in C++ for high performance with a Python interface, QuAK delivers real-time, interpretable verification feedback. As the first quantitative automata analysis platform offering completeness, scalability, and debuggability, QuAK significantly advances the state of the art in quantitative system verification.

Technology Category

• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

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.

Problem

• Quantitative Automata Analysis
• Automata Performance Evaluation
• Uncertainty Handling

Innovation

• QuAK Software Tool
• Quantitative Automata Analysis
• Uncertainty Handling