Abstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis

Towards the goal of correctness and reliability of hybrid systems, we continue our nonstandard static analysis program (with Suenaga and Sekine) where hybrid dynamics is turned into purely discrete one with explicit use of infinitesimals. While our previous results have focused on deductive verification by program logics, the current work aims at automation and enhanced scalability by extending abstract interpretation—a technique known for its ample scalability and widespread use in various verification tools—with infinitesimals. Our theoretical results include soundness and termination via uniform widening operators; and our prototype implementation successfully verifies some benchmark examples.