Applications of automata learning in verification and synthesis

The objective of this thesis is to explore automata learning, which is an umbrella term for techniques that derive finite automata from external information sources, in the areas of verification and synthesis. We consider four application scenarios that turn out to be particularly well-suited: Regular Model Checking, quantified invariants of linear data structures, automatic reachability games, and labeled safety games. The former two scenarios stem from the area of verification whereas the latter two stem from the area of synthesis (more precisely, from the area of infinite-duration two-player games over graphs, as popularized by McNaughton). Regular Model Checking is a special kind of Model Checking in which the program to verify is modeled in terms of finite automata. We develop various (semi-)algorithms for computing invariants in Regular Model Checking: a white-box algorithm, which takes the whole program as input; two semi-black-box algorithms, which have access to a part of the program and learn missing information from a teacher; finally, two black-box algorithms, which obtain all information about the program from a teacher. For the black-box algorithms, we employ a novel paradigm, called ICE-learning, which is a generic learning setting for learning invariants. Quantified invariants of linear data structures occur in Floyd-Hoare-style verification of programs manipulating arrays and lists. To learn such invariants, we introduce the notion of quantified data automata and develop an active learning algorithm for these automata. Based on a finite sample of configurations that manifest on executions of the program in question, we learn a quantified data automaton and translate it into a logic formula expressing the invariant. The latter potentially requires an additional abstraction step to ensure that the resulting formula falls into a decidable logic. Automatic reachability games are classical reachability games played over automatic graphs; automatic graphs are defined by means of asynchronous transducers and subsume various types of graphs, such as finite graphs, pushdown graphs, and configuration graphs of Turing machines. We first consider automatic reachability games over finite graphs and present a symbolic fixed-point algorithm for computing attractors that uses deterministic finite automata to represent sets of vertices. Since such a