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We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain is approximately equivalent to the original system in a distributional sense. Approximate equivalence of the stochastic hybrid system and its Markov chain reduction means that analyzing the Markov chain with respect to a suitably strengthened property, allows us to conclude whether the original stochastic hybrid system meets its temporal logic specifications. We present the first statistical model checking algorithms to verify stochastic hybrid systems against correctness properties, expressed in the linear inequality linear temporal logic (iLTL) or the metric interval temporal logic (MITL).

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems., Comment: NeurIPS 2019

Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov Decision Processes (MDPs) by sampling, e.g., checking whether there exists a feasible policy such that the probability of reaching certain goal states is greater than a threshold. We use reinforcement learning to search for such a feasible policy for PCTL specifications, and then develop a statistical model checking (SMC) method with provable guarantees on its error. Specifically, we first use upper-confidence-bound (UCB) based Q-learning to design an SMC algorithm for bounded-time PCTL specifications, and then extend this algorithm to unbounded-time specifications by identifying a proper truncation time by checking the PCTL specification and its negation at the same time. Finally, we evaluate the proposed method on case studies.

Metric Interval Temporal Logic (MITL) is a well studied real-time, temporal logic that has decidable satisfiability and model checking problems. The decision procedures for MITL rely on the automata theoretic approach, where logic formulas are translated into equivalent timed automata. Since timed automata are not closed under complementation, decision procedures for MITL first convert a formula into negated normal form before translating to a timed automaton. We show that, unfortunately, these 20-year-old procedures are incorrect, because they rely on an incorrect semantics of the R operator. We present the right semantics of R and give new, correct decision procedures for MITL. We show that both satisfiability and model checking for MITL are EXPSPACE-complete, as was previously claimed. We also identify a fragment of MITL that we call MITL_{WI} that is richer than MITL_{0,\infty}, for which we show that both satisfiability and model checking are PSPACE-complete. Many of our results have been formally proved in PVS., Comment: Presented at the 19th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI'18)

Industrial cyber-physical systems are hybrid systems with strict safety requirements. Despite not having a formal semantics, most of these systems are modeled using Stateflow/Simulink for mainly two reasons: (1) it is easier to model, test, and simulate using these tools, and (2) dynamics of these systems are not supported by most other tools. Furthermore, with the ever growing complexity of cyber-physical systems, grows the gap between what can be modeled using an automatic formal verification tool and models of industrial cyber-physical systems. In this paper, we present a simple formal model for self-deriving cars. While after some simplification, safety of this system has already been proven manually, to the best of our knowledge, no automatic formal verification tool supports its dynamics. We hope this serves as a challenge problem for formal verification tools targeting industrial applications., Comment: 7 pages