HyperCertificates: Verification of Discrete-time Dynamical Systems against HyperLTL Specifications
Certify multi-trace system properties like opacity and privacy automatically…
A new paper by Vishnu Murali, Amin Falah, Ashutosh Trivedi, and Majid Zamani (arXiv:2605.00752) proposes HyperCertificates, a novel technique for verifying discrete-time dynamical systems against hyperproperties—specifications that compare multiple execution traces. Traditional linear temporal logic (LTL) only checks a single trace, but HyperLTL extends LTL to capture relationships between traces, making it ideal for security properties like opacity, privacy, and robustness. The HyperCertificate framework consists of two functions: a lookahead function (implemented via closure certificates) and a combined barrier and ranking function that provides inductive guarantees modulo that lookahead.
The approach is automatable using sum-of-squares (SOS) optimization and satisfiability modulo theories (SMT) solvers, enabling practical deployment without hand-crafted proofs. The authors demonstrate the method on several case studies (24-page paper, 3 figures). For practitioners, this means a formal, machine-checkable way to certify that a discrete-time controller or cyber-physical system respects cross-trace properties—critical for safety-critical applications where system behavior must be provably private or robust against adversaries. The work bridges control theory and formal methods, offering a concrete path to automation.
- Defines HyperCertificates as a pair of functions (lookahead + barrier/ranking) to verify HyperLTL specifications on discrete-time dynamical systems.
- Automatable via SOS optimization and SMT solvers – reduces manual verification effort.
- Demonstrated on case studies addressing opacity, privacy, and robustness – directly applicable to security-critical control systems.
Why It Matters
Enables automated, provable guarantees on multi-trace properties for safety-critical systems like autonomous vehicles and industrial controllers.