Optimal LTLf Synthesis
For researchers in formal methods and automated synthesis, this work provides a practical approach to handling unrealisable specifications by maximizing realized objectives.
The paper introduces optimal LTLf synthesis, which aims to realize as many objectives as possible when not all are jointly realisable, proposing max-guarantee, max-observation, and incremental max-observation synthesis. Experiments show these variations scale well, solving most benchmark instances within timeout.
Strategy synthesis typically follows an all-or-nothing paradigm, returning unrealisable whenever a specification cannot be guaranteed in an uncertain environment. In this paper, we introduce optimal LTLf synthesis, where the goal is to realise as many objectives as possible from a given specification consisting of multiple objectives, especially for the case that they are not all jointly realisable. We first consider max-guarantee synthesis, which commits to a maximal set of objectives that we can a priori guarantee to realise. We then introduce max-observation synthesis, which maximises a posteriori realised objectives that may be incomparable on different executions. Finally, we present incremental max-observation synthesis, which further improves strategies by exploiting opportunities for stronger guarantees when they arise during an execution. Experimental results show that different variations of optimal synthesis scale broadly equally well, solving a large fraction of the benchmark instances within the given timeout, demonstrating the practical feasibility of the approach.