Optimal LTLf Synthesis

TL;DR

This paper introduces optimal LTLf synthesis methods that aim to maximize the number of objectives realized in uncertain environments, improving strategy quality over traditional all-or-nothing approaches.

Contribution

It proposes max-guarantee, max-observation, and incremental max-observation synthesis techniques for more flexible and practical LTLf strategy synthesis.

Findings

Different synthesis variations scale well on benchmarks.

The approaches solve a large fraction of instances within time limits.

Experimental results demonstrate practical feasibility of the methods.

Abstract

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.