LTLf Synthesis under Partial Observability: From Theory to Practice

Abstract

LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the difficulty of implementing such an extension in practice means that it has remained in the realm of theory. Recently, it has been demonstrated that restricting LTL synthesis to systems with finite executions by using LTL with finite-horizon semantics (LTLf) allows for significantly simpler implementations in practice. With the conceptual simplicity of LTLf, it becomes possible to explore extensions such as partial observability in practice for the first time. Previous work has analyzed the problem of LTLf synthesis under partial observability theoretically and suggested two possible algorithms, one with 3EXPTIME and another with 2EXPTIME complexity. In this work, we first prove a complexity lower bound conjectured in earlier work. Then, we complement the theoretical analysis by showing how the two algorithms can be integrated in practice into an established framework for LTLf synthesis. We furthermore identify a third, MSO-based, approach enabled by this framework. Our experimental evaluation reveals very different results from what the theory seems to suggest, with the 3EXPTIME algorithm often outperforming the 2EXPTIME approach. Furthermore, as long as it is able to overcome an initial memory bottleneck, the MSO-based approach can often outperforms the others.