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Hiroshi Unno

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AAAI Conference 2025 Conference Paper

Solving Higher-Order Quantified Boolean Satisfiability via Higher-Order Model Checking

  • Hiroshi Unno
  • Takeshi Tsukada
  • Jie-Hong Roland Jiang

The satisfiability (SAT) problem of higher-order quantified Boolean formula (HOQBF) emerged as a natural generalization of SAT, quantified SAT, and second-order quantified SAT. It allows succinct encoding of k-EXPTIME problems beyond the reach of prior Boolean satisfiability formulations, but its application was hampered by the lack of solvers. In this paper, we present the first HOQBF solver that leverages techniques from the model-checking community. Our HOQBF solver is based on reduction to higher-order model checking, which is a generalization from model checking of while-programs to that of higher-order functional programs. The ability of a higher-order model checker to deal with higher-order functions in a program is used to reason about higher-order quantifiers in HOQBF.

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AAAI Conference 2020 Conference Paper

Probabilistic Inference for Predicate Constraint Satisfaction

  • Yuki Satake
  • Hiroshi Unno
  • Hinata Yanagi

In this paper, we present a novel constraint solving method for a class of predicate Constraint Satisfaction Problems (pCSP) where each constraint is represented by an arbitrary clause of first-order predicate logic over predicate variables. The class of pCSP properly subsumes the well-studied class of Constrained Horn Clauses (CHCs) where each constraint is restricted to a Horn clause. The class of CHCs has been widely applied to verification of linear-time safety properties of programs in different paradigms. In this paper, we show that pCSP further widens the applicability to verification of branching-time safety properties of programs that exhibit finitely-branching non-determinism. Solving pCSP (and CHCs) however is challenging because the search space of solutions is often very large (or unbounded), highdimensional, and non-smooth. To address these challenges, our method naturally combines techniques studied separately in different literatures: counterexample guided inductive synthesis (CEGIS) and probabilistic inference in graphical models. We have implemented the presented method and obtained promising results on existing benchmarks as well as new ones that are beyond the scope of existing CHC solvers.

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v2026.09.13