QuAK: Quantitative Automata Kit

2024-09-05

Leveraging Applications of Formal Methods

AI Summary

Traditional binary correctness verification fails to capture quantitative system behaviors. Method: We propose the first automated toolkit for quantitative automata supporting six classical semantics—Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg—and systematically address core decision problems: emptiness, inclusion, equivalence, and safety/liveness verification. Our approach introduces weighted transition modeling and a generalized value-function framework, integrating symbolic decision procedures, optimization solvers, and automata transformation techniques to enable extremal-value computation, safety-liveness decomposition, and real-time monitoring. Contribution/Results: Experiments demonstrate efficiency on inclusion checking, constant-function recognition, and online monitoring tasks. We release the first open-source benchmark suite for quantitative automata analysis, establishing a scalable, modular, and unified infrastructure for quantitative system verification.

Technology Category

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

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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 Inf, Sup, LimInf, LimSup, LimInfAvg, and 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.

Problem

• Analyzing quantitative aspects of system behaviors
• Automating analysis of various quantitative automata types
• Solving decision problems like emptiness and inclusion

Innovation

• Automates analysis of quantitative automata
• Supports multiple quantitative automaton types
• Implements decision procedures for automaton problems