The deployment of Artificial Neural Networks (ANNs) in safety-critical applications poses a number of new verification and certification challenges. In particular, for ANN-enabled self-driving vehicles it is important to establish properties about the resilience of ANNs to noisy or even maliciously manipulated sensory input. We are addressing these challenges by defining resilience properties of ANN-based classifiers as the maximum amount of input or sensor perturbation which is still tolerated. This problem of computing maximum perturbation bounds for ANNs is then reduced to solving mixed integer optimization problems (MIP). A number of MIP encoding heuristics are developed for drastically reducing MIP-solver runtimes, and using parallelization of MIP-solvers results in an almost linear speed-up in the number (up to a certain limit) of computing cores in our experiments. We demonstrate the effectiveness and scalability of our approach by means of computing maximum resilience bounds for a number of ANN benchmark sets ranging from typical image recognition scenarios to the autonomous maneuvering of robots.

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We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step requires quantifier-elimination, and we propose a lazy quantifierelimination procedure, which delays expensive computations of disjunctive normal forms when possible. The effectiveness of induction based on bounded model checking and invariant strengthening is demonstrated using infinite-state systems ranging from communication protocols to timed automata and (linear) hybrid automata.

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