Non-linear Continuous Systems for Safety Verification (Benchmark Proposal)

Safety verification of hybrid dynamical systems relies crucially on the ability to reason about reachable sets of continuous systems whose evolution is governed by a system of ordinary differential equations (ODEs). Verification tools are often restricted to handling a particular class of continuous systems, such as e.g. differential equations with constant right-hand sides, or systems of affine ODEs. More recently, verification tools capable of working with non-linear differential equations have been developed. The behavior of non-linear systems is known to be in general extremely difficult to analyze because solutions are rarely available in closed-form. In order to assess the practical utility of the various verification tools working with non-linear ODEs it is very useful to maintain a set of verification problems. Similar efforts have been successful in other communities, such as automated theorem proving, SAT solving and numerical analysis, and have accelerated improvements in the tools and their underlying algorithms. We present a set of 65 safety verification problems featuring non-linear polynomial ODEs and for which we have proofs of safety. We discuss the various issues associated with benchmarking the currently available verification tools using these problems.