Heuristics for the refinement of assumptions in generalized reactivity formulae

Reactive synthesis is concerned with automatically generating implementations from formal specifications. These specifications are typically written in the language of generalized reactivity (GR(1)), a subset of linear temporal logic capable of expressing the most common industrial specification patterns, and describe the requirements about the behavior of a system under assumptions about the environment where the system is to be deployed. Oftentimes no implementation exists which guarantees the required behavior under all possible environments, typically due to missing assumptions (this is usually referred to as unrealizability). To address this issue, new assumptions need to be added to complete the specification, a problem known as assumptions refinement. Since the space of candidate assumptions is intractably large, searching for the best solutions is inherently hard. In particular, new methods are needed to (i) increase the effectiveness of the search procedures, measured as the ratio between the number of solutions found and of refinements explored; and (ii) improve the results' quality, defined as the weakness of the solutions. In this thesis we propose a set of heuristics to meet these goals, and a methodology to assess and compare assumptions refinement methods based on quantitative metrics. The heuristics are in the form of algorithms to generate candidate refinements during the search, and quantitative measures to assess the quality of the candidates. We first discuss a heuristic method to generate assumptions that target the cause of unrealizability. This is done by selecting candidate refinement formulas based on Craig's interpolation. We provide a formal underpinning of the technique and evaluate it in terms of our new metric of effectiveness, as defined above, whose value is improved with respect to the state of the art. We demonstrate this on a set of popular benchmarks of embedded software. We then provide a formal, quantitative characterization of the permissiveness of environment assumptions in the form of a weakness measure. We prove that the partial order induced by this measure is consistent with the one induced by implication. The key advantage of this measure is that it allows for prioritizing candidate solutions, as we show experimentally. Lastly, we propose a notion of minimal refinements with respect to the observed counterstrategies. We demonstrate that exploring minimal refinements produces weaker solutions, and reduces the amount of computations needed to explore each refinement. However, this may come at the cost of reducing the effectiveness of the search. To counteract this effect, we propose a hybrid search approach in which both minimal and non-minimal refinements are explored.Open Acces