Abstract We present the OGAN algorithm for automatic requirement falsification of cyber-physical systems. System inputs and outputs are represented as piecewise constant signals over time while requirements are expressed in signal temporal logic. OGAN can find inputs that are counterexamples for the correctness of a system revealing design, software, or hardware defects before the system is taken into operation. The OGAN algorithm works by training a generative machine learning model to produce such counterexamples. It executes tests offline and does not require any previous model of the system under test. We evaluate OGAN using the ARCH-COMP benchmark problems, and the experimental results show that generative models are a viable method for requirement falsification. OGAN can be applied to new systems with little effort, has few requirements for the system under test, and exhibits state-of-the-art CPS falsification efficiency and effectiveness.

To each one-dimensional subshift X, we may associate a winning shift W(X) which arises from a combinatorial game played on the language of X. Previously it has been studied what properties of X does W(X) inherit. For example, X and W(X) have the same factor complexity and if X is a sofic subshift, then W(X) is also sofic. In this paper, we develop a notion of automaticity for W(X), that is, we propose what it means that a vector representation of W(X) is accepted by a finite automaton. Let S be an abstract numeration system such that addition with respect to S is a rational relation. Let X be a subshift generated by an S-automatic word. We prove that as long as there is a bound on the number of nonzero symbols in configurations of W(X) (which follows from X having sublinear factor complexity), then W(X) is accepted by a finite automaton, which can be effectively constructed from the description of X. We provide an explicit automaton when X is generated by certain automatic words such as the Thue-Morse word.