2019/08/27 by Youkichi Hosoi, Naoki Kobayashi, Hosoi, Youkichi +3
Computer Science · #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Programming Languages (cs.PL)
paper · pdf · doi:10.48550/arxiv.1908.10416
openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal mu-calculus, and strictly more expressive than the modal mu-calculus. It has recently been shown that various program verification problems can naturally be reduced to HFL model checking: the problem of whether a given finite state system satisfies a given HFL formula. In this paper, we propose a novel algorithm for HFL model checking: it is the first practical algorithm in that it runs fast for typical inputs, despite the hyper-exponential worst-case complexity of the HFL model checking problem. Our algorithm is based on Kobayashi et al.'s type-based characterization of HFL model checking, and was inspired by a saturation-based algorithm for HORS model checking, another higher-order extension of model checking. We prove the correctness of the algorithm and report on an implementation and experimental results.