Combined Global and Local Search for the Falsification of Hybrid Systems

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for achieving both efficiency and global convergence. In local search, it exploits derivatives for efficient computation. Unlike other methods for falsification of hybrid systems with deterministic evolution, we do not restrict our search to trajectories of a certain bounded length but search for error trajectories of arbitrary length

Time-Staging Enhancement of Hybrid System Falsification

Optimization-based falsification employs stochastic optimization algorithms to search for error input of hybrid systems. In this paper we introduce a simple idea to enhance falsification, namely time staging, that allows the time-causal structure of time-dependent signals to be exploited by the optimizers. Time staging consists of running a falsification solver multiple times, from one interval to another, incrementally constructing an input signal candidate. Our experiments show that time staging can dramatically increase performance in some realistic examples. We also present theoretical results that suggest the kinds of models and specifications for which time staging is likely to be effective

Enhancing Temporal Logic Falsification of Cyber-Physical Systems using multiple objective functions and a new optimization method

Cyber-physical systems (CPSs) are engineering systems that bridge the cyber-world of communications and computing with the physical world. These systems are usually safety-critical and exhibit both discrete and continuous dynamics that may have complex behavior. Typically, these systems have to satisfy given specifications, i.e., properties that define the valid behavior. One commonly used approach to evaluate the correctness of CPSs is testing. The main aim of testing is to detect if there are situations that may falsify the specifications.\ua0For many industrial applications, it is only possible to simulate the system under test because mathematical models do not exist, thus formal verification is not a viable option. Falsification is a strategy that can be used for testing CPSs as long as the system can be simulated and formal specifications exist. Falsification attempts to find counterexamples, in the form of input signals and parameters, that violate the specifications of the system. Random search or optimization can be used for the falsification process. In the case of an optimization-based approach, a quantitative semantics is needed to associate a simulation with a measure of the distance to a specification being falsified. This measure is used to guide the search in a direction that is more likely to falsify a specification, if possible. \ua0The measure can be defined in different ways. In this thesis, we evaluate different quantitative semantics that can be used to define this measure. The efficiency of the falsification can be affected by both the quantitative semantics used and the choice of the optimization method. The presented work attempts to improve the efficiency of the falsification process by suggesting to use multiple quantitative semantics, as well as a new optimization method. The use of different quantitative semantics and the new optimization method have been evaluated on standard benchmark problems. We show that the proposed methods improve the efficiency of the falsification process

On Optimization-Based Falsification of Cyber-Physical Systems

In what is commonly referred to as cyber-physical systems (CPSs), computational and physical resources are closely interconnected. An example is the closed-loop behavior of perception, planning, and control algorithms, executing on a computer and interacting with a physical environment. Many CPSs are safety-critical, and it is thus important to guarantee that they behave according to given specifications that define the correct behavior. CPS models typically include differential equations, state machines, and code written in general-purpose programming languages. This heterogeneity makes it generally not feasible to use analytical methods to evaluate the system’s correctness. Instead, model-based testing of a simulation of the system is more viable. Optimization-based falsification is an approach to, using a simulation model, automatically check for the existence of input signals that make the CPS violate given specifications. Quantitative semantics estimate how far the specification is from being violated for a given scenario. The decision variables in the optimization problems are parameters that determine the type and shape of generated input signals. This thesis contributes to the increased efficiency of optimization-based falsification in four ways. (i) A method for using multiple quantitative semantics during optimization-based falsification. (ii) A direct search approach, called line-search falsification that prioritizes extreme values, which are known to often falsify specifications, and has a good balance between exploration and exploitation of the parameter space. (iii) An adaptation of Bayesian optimization that allows for injecting prior knowledge and uses a special acquisition function for finding falsifying points rather than the global minima. (iv) An investigation of different input signal parameterizations and their coverability of the space and time and frequency domains. The proposed methods have been implemented and evaluated on standard falsification benchmark problems. Based on these empirical studies, we show the efficiency of the proposed methods. Taken together, the proposed methods are important contributions to the falsification of CPSs and in enabling a more efficient falsification process