Compositional Verification of Timed Automata via Violation Assumptions

Abstract In many verification tasks, system models do not correspond to the focused and idealized models that appear in research literature. In practice, models usually contain components and execution paths that are irrelevant to the property being verified or have only a limited effect on it. Compositional verification presents a practical method for coping with the larger and less targeted models found in such settings. In this paper, we present an automated compositional framework for verifying timed safety properties in networks of timed automata. We show as a main result that the weakest environment assumption, commonly used in compositional reasoning, may in general fail to be recognizable within the timed automata formalism. This negative result motivates shifting the focus to the complement language of violation-inducing timed words, for which we establish recognizability using timed automata with silent transitions. We provide an algorithm for its construction and reduce its size by retaining only the parts directly relevant to the property. The synthesized assumption is later applied to verify the original system. This provides a sound and complete basis for compositional verification of timed automata, including the novel ability to handle automata with multiple clocks and non-deterministic behavior. Our results broaden the applicability of assume–guarantee verification techniques in timed automata and show substantial reductions in the size of the state-space, outperforming monolithic methods on a range of case studies.