Optimal LTLf Synthesis

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.

Good-for-MDP State Reduction for Stochastic LTL Planning

We study stochastic planning problems in Markov Decision Processes (MDPs) with goals specified in Linear Temporal Logic (LTL). The state-of-the-art approach transforms LTL formulas into good-for-MDP (GFM) automata, which feature a restricted form of nondeterminism. These automata are then composed with the MDP, allowing the agent to resolve the nondeterminism during policy synthesis. A major factor affecting the scalability of this approach is the size of the generated automata. In this paper, we propose a novel GFM state-space reduction technique that significantly reduces the number of automata states. Our method employs a sophisticated chain of transformations, leveraging recent advances in good-for-games minimisation developed for adversarial settings. In addition to our theoretical contributions, we present empirical results demonstrating the practical effectiveness of our state-reduction technique. Furthermore, we introduce a direct construction method for formulas of the form $\mathsf{G}\mathsf{F}\varphi$, where $\varphi$ is a co-safety formula. This construction is provably single-exponential in the worst case, in contrast to the general doubly-exponential complexity. Our experiments confirm the scalability advantages of this specialised construction.