Download PDFOpen PDF in browserInduction and K-Induction for Hyperproperties19 pages•Published: October 23, 2026AbstractHyperproperties, which express system behaviors that relate multiple execution traces, cover a variety of important safety and security properties. Among these, hyperproperties of the form ∀∃.φ, where φ is an invariant or a SafetyLTL formula, capture many practically relevant specifications including noninterference, symmetry, and robust path planning. Despite their importance, efficient verification algorithms for such properties remain limited. In this paper, we propose novel verification algorithms for such ∀∃-hyperproperties. Our approach extends classical induction and k-induction techniques, widely used in single-trace verification, to the hyperproperty setting. We develop hyper-inductive reasoning principles that generalize the base and step cases of induction to sets of traces, refinement techniques to strengthen the property, and incremental approaches to increasing the bound of the k-induction. As a byproduct, we introduce hyper-(k)-inductive invariants, as certificates to witness satisfaction of ∀∃-hyperproperties over transition systems. We evaluate our approach on various benchmarks, demonstrating that our methods are complementary to state-of-the-art hyperproperty model checkers, and we analyze in which cases one option prevails over the others.Keyphrases: hyperltl, induction, k induction, model checking In: Erika Ábrahám, Nikolaj Bjørner and Michael Rawson (editors). Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning, vol 112, pages 127-145.
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