Optimal LTLf Synthesis

2026-05-12

AI Summary

When a multi-objective LTLf specification is globally unrealizable, traditional synthesis methods merely return “unrealizable” and fail to achieve any feasible subset of objectives. This work formally introduces and systematically addresses the problem of partial realizability for multi-objective LTLf specifications, proposing three optimal synthesis paradigms: max-guarantee (maximizing guaranteed satisfaction a priori), max-observation (maximizing satisfied objectives a posteriori based on observed outcomes), and incremental max-observation (dynamically optimizing objective satisfaction during execution). The approach integrates LTLf automata theory and game semantics, combining formal verification with dynamic strategy optimization. Experimental results demonstrate that the proposed methods are efficient, scalable, and effective in maximizing the number of achieved subgoals on standard benchmarks, significantly enhancing practical utility under unrealizable specifications.

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.

Problem

• LTLf synthesis
• optimal synthesis
• unrealisable specifications
• multi-objective synthesis
• strategy synthesis

Innovation

• optimal LTLf synthesis
• max-guarantee synthesis
• max-observation synthesis
• incremental synthesis
• strategy synthesis