Houssam Abbas

Probabilistic Temporal Logic Falsification of Cyber-Physical Systems

We present a Monte-Carlo optimization technique for finding system behaviors that falsify a metric temporal logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a falsifying behavior by exploring trajectories with smaller robustness values. The resulting testing framework can be applied to a wide class of cyber-physical systems (CPS). We show through experiments on complex system models that using our framework can help automatically falsify properties with more consistency as compared to other means, such as uniform sampling.

Formal property verification in a conformance testing framework

In model-based design of cyber-physical systems, such as switched mixed-signal circuits or software-controlled physical systems, it is common to develop a sequence of system models of different fidelity and complexity, each appropriate for a particular design or verification task. In such a sequence, one model is often derived from the other by a process of simplification or implementation. E.g. a Simulink model might be implemented on an embedded processor via automatic code generation. Three questions naturally present themselves: how do we quantify closeness between the two systems? How can we measure such closeness? If the original system satisfies some formal property, can we automatically infer what properties are then satisfied by the derived model? This paper addresses all three questions: we quantify the closeness between original and derived model via a distance measure between their outputs. We then propose two computational methods for approximating this closeness measure. Finally, we derive syntactical re-writing rules which, when applied to a Metric Temporal Logic specification satisfied by the original model, produce a formula satisfied by the derived model. We demonstrate the soundness of the theory with several experiments.

Computing descent direction of MTL robustness for non-linear systems

The automatic analysis of transient properties of nonlinear dynamical systems is a challenging problem. The problem is even more challenging when complex state-space and timing requirements must be satisfied by the system. Such complex requirements can be captured by Metric Temporal Logic (MTL) specifications. The problem of finding system behaviors that do not satisfy an MTL specification is referred to as MTL falsification. This paper presents an approach for improving stochastic MTL falsification methods by performing local search in the set of initial conditions. In particular, MTL robustness quantifies how correct or wrong is a system trajectory with respect to an MTL specification. Positive values indicate satisfaction of the property while negative values indicate falsification. A stochastic falsification method attempts to minimize the systems robustness with respect to the MTL property. Given some arbitrary initial state, this paper presents a method to compute a descent direction in the set of initial conditions, such that the new system trajectory gets closer to the unsafe set of behaviors. This technique can be iterated in order to converge to a local minimum of the robustness landscape. The paper demonstrates the applicability of the method on some challenging nonlinear systems from the literature.

Suppression of Mosquito Noise by Recursive Epsilon-Filters

This work addresses the problem of mosquito noise (MN) reduction in compressed video sequences. A compression-blind approach is adopted; the advantage of such an approach is that it is independent of the particular compressor used and of its particular settings. A recursive filtering scheme is presented. It is shown how the filtering parameter ϵ can be adaptively selected to maximize the denoising performance by minimizing the number of outlier pixels in the filters support. Simulation results show that the proposed blind MN-denoising scheme outperforms existing MN-denoising methods.

Robustness-guided temporal logic testing and verification for Stochastic Cyber-Physical Systems

We present a framework for automatic specification-guided testing for Stochastic Cyber-Physical Systems (SCPS). The framework utilizes the theory of robustness of Metric Temporal Logic (MTL) specifications to quantify how robustly an SCPS satisfies a specification in MTL. The goal of the testing framework is to detect system operating conditions that cause the system to exhibit the worst expected specification robustness. The resulting expected robustness minimization problem is solved using Markov chain Monte Carlo algorithms. This also allows us to use finite-time guarantees, which quantify the quality of the solution after a finite number of simulations. In a Model-Based Design (MBD) process, our framework can be combined with Statistical Model Checking (SMC). Finally, we present a case study on a high fidelity engine model where the goal is to verify the air-to-fuel ratio problem.

Linear hybrid system falsification through local search

In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, given a sequence of locations and a maximum simulation time, we return the trajectory that comes closest to the unsafe set. This problem is formulated as a differentiable optimization problem and solved. The purpose of developing such a local search method is to combine it with high level stochastic optimization algorithms in order to falsify hybrid systems with complex discrete dynamics and high dimensional continuous spaces. Experimental results indicate that the local search procedure improves upon the results of pure stochastic optimization algorithms.

Functional gradient descent method for Metric Temporal Logic specifications

Metric Temporal Logic (MTL) specifications can capture complex state and timing requirements. Given a nonlinear dynamical system and an MTL specification for that system, our goal is to find a trajectory that violates or satisfies the specification. This trajectory can be used as a concrete feedback to the system designer in the case of violation or as a trajectory to be tracked in the case of satisfaction. The search for such a trajectory is conducted over the space of initial conditions, system parameters and input signals. We convert the trajectory search problem into an optimization problem through MTL robust semantics. Robustness quantifies how close the trajectory is to violating or satisfying a specification. Starting from some arbitrary initial condition and parameter and given an input signal, we compute a descent direction in the search space, which leads to a trajectory that optimizes the MTL robustness. This process can be iterated to reach local optima (min or max). We demonstrate the method on examples from the literature.

Convergence proofs for Simulated Annealing falsification of safety properties

The problem of falsifying temporal logic properties of hybrid automata can be posed as a minimization problem by utilizing quantitative semantics for temporal logics. Previous work has used a variation of Simulated Annealing (SA) to solve the problem. While SA is known to converge to the global minimum of a continuous objective function over a closed and bounded search space, or when the search space is discrete, there do not exist convergence proofs for the cases addressed in that previous work. Namely, when the objective function is discontinuous, and when the objective is a vector-valued function. In this paper, we derive conditions and we prove convergence of SA to a global minimum in both scenarios. We also consider matters affecting the practical performance of SA.

WiP abstract: Conformance Testing as Falsification for Cyber-Physical Systems

In a typical Model-Based Design (MBD) process for Cyber-Physical Systems, an initial `simple Model is successively refined and made more accurate and complex; then it is implemented on a real-time computational platform, and further modified to yield an Implementation. The goal is to produce a system that satisfies a formal specification Φ. This successive refinement raises the question of how “close” are the “simple” Model and the“complex”Implementation. Answering this question is important because it is not always possible to verify formally that the Implementation satisfies the specification Φ. Moreover, even if the Implementation satisfies Φ, it will have unspecified behavior which might exhibit bugs. By quantifying the `closeness between Model and Implementation, our level of confidence in the Implementation derives from our confidence in the Model, and the fact that the Model satisfies Φ.