HyperCertificates: Verification of Discrete-time Dynamical Systems against HyperLTL Specifications

2026-05-01

AI Summary

This work addresses the verification of HyperLTL hyperproperties—such as privacy, opacity, and robustness—for discrete-time dynamical systems, where such properties inherently capture relational behaviors across multiple execution traces. To this end, the paper introduces a functional induction framework based on HyperCertificates, which for the first time extends barrier and ranking function techniques to the setting of HyperLTL verification. A key innovation is the incorporation of closure certificates to formally model forward-looking dependencies among traces. The proposed approach integrates sum-of-squares (SOS) optimization with SMT solving to enable fully automated verification. Experimental evaluation demonstrates that the framework is both effective and scalable across several case studies, offering formal guarantees for properties involving intricate multi-trace dependencies.

Abstract

We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae which are concerned with individual traces of a system, hyperproperties are properties that are concerned with how the traces of a system relate to one another. HyperLTL is an extension of LTL for hyperproperties, and is useful to describe specifications such as opacity, privacy as well as notions of robustness. Our notion of HyperCertificates consists of a pair of functions, where the first models the lookahead, and the second relies on a combination of barrier and ranking functions. We use closure certificates, to act as a model for this lookahead and then rely on barrier and ranking function arguments modulo this lookahead to provide guarantees against HyperLTL formulae. We demonstrate how our approach is automatable via existing techniques such as sum-of-squares optimization (SOS) and satisfiability modulo theories (SMT) solvers. Finally, we demonstrate our approach on some case studies.

Problem

• Hyperproperties
• HyperLTL
• Discrete-time dynamical systems
• Verification
• Temporal logic

Innovation

• HyperCertificates
• HyperLTL
• barrier functions
• ranking functions
• discrete-time dynamical systems