Monitoring of spatio-temporal properties with nonlinear SAT solvers

The automotive industry is increasingly dependent on computing systems with different critical requirements. The verification and validation methods for these systems are now leveraging complex AI methods, for which the decision algorithms introduce non-determinism, especially in autonomous driving. This paper presents a runtime verification technique agnostic to the target system, which focuses on monitoring spatio-temporal properties that abstract the evolution of objects' behavior in their spatial and temporal flow. First, a formalization of three known traffic rules (from the Vienna convention on road traffic) is presented, where a spatio-temporal logic fragment is used. Then, these logical expressions are translated to a monitoring model written in first-order logic, where they are processed by a non-linear satisfiability solver. Finally, the translation allows the solver to check the validity of the encoded properties according to an instance of a specific traffic scenario (a trace). The results obtained from our tool, which automatically generates a monitor from a formula, show that our approach is feasible for online monitoring in a real-world environment.