Abstract

We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose right-hand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required differential invariants. As a means for combining local differential invariants into global system invariants in a sound way, our fixedpoint algorithm works with a compositional verification logic for hybrid systems. With this compositional approach we exploit locality in system designs. To improve the verification power, we further introduce a saturation procedure that refines the system dynamics successively with differential invariants until safety becomes provable. By complementing our symbolic verification algorithm with a robust version of numerical falsification, we obtain a fast and sound verification procedure. We verify roundabout maneuvers in air traffic management and collision avoidance in train control and car control. Document type: Part of book or chapter of book

Abstract

The productivity and scalability of verifying pipelined circuits can be increased by exploiting the structural and behavioural characteristics that distinguish pipelines from other circuits. This paper presents a formal model of pipelines that augments a state machine with information to describe the transfer of parcels between stages, and reading and writing state variables. Using our model, we created a definition of correctness that is based on the well-established principles of structural, control, and data hazards. We have proved that any pipeline that satisfies our hazards-based definition of correctness is guaranteed to satisfy the conventional correctness statement of Burch-Dill style flushing. Document type: Part of book or chapter of book