Random Generation of Small Quantitative Automata for Algorithm Debugging

2026-07-13

AI Summary

Analysis algorithms for quantitative automata are often complex and prone to subtle implementation bugs that existing testing approaches struggle to expose effectively. This work proposes a debugging framework that integrates non-degenerate random generation, property validation, and automated counterexample minimization to efficiently produce small, actionable counterexamples. Applied to implementations of parametric timed automata, the method successfully uncovered five previously unknown bugs in IMITATOR, a mainstream model checking tool. Notably, the simplest counterexample involves only two locations and one transition, demonstrating a significant improvement in both bug detection capability and debugging efficiency.

Abstract

Analysis algorithms for quantitative automata are complex and hard to validate. Existing approaches -- benchmarks, mutation testing, uniform random generation -- each fail to expose subtle implementation bugs. We present a framework that repeatedly 1) generates random quantitative automata that are non-degenerate by construction, 2) tests each against a target property, and 3) shrinks any violation to a local minimum, yielding a small, actionable counterexample. We implement the framework for parametric timed automata (PTA) and apply it to IMITATOR, a mature model checker for PTA, uncovering 5 previously unknown bugs, one of which was exposed by a counterexample with just 2 locations and 1 transition.

Problem

• quantitative automata
• algorithm debugging
• implementation bugs
• random generation
• model checking

Innovation

• quantitative automata
• random generation
• counterexample minimization
• parametric timed automata
• algorithm debugging