# How undecidable are HyperLTL and HyperCTL*?

- Speaker(s)
**Marie Fortin**- Affiliation
- University of Liverpool
- Date
- March 9, 2022, 2:15 p.m.
- Information about the event
- Online
- Seminar
- Seminar Automata Theory

Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. Two of the most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by trace quantification. It is known that this expressiveness comes at a price, i.e., satisfiability is undecidable for both logics. We settle the exact complexity of these problems, showing that both are in fact highly undecidable: we prove that HyperLTL satisfiability is \Sigma^1_1-complete and HyperCTL* satisfiability is \Sigma^2_1-complete. To prove \Sigma^2_1 membership for HyperCTL*, we prove that every satisfiable HyperCTL* formula has a model that is equinumerous to the continuum, the first upper bound of this kind. We prove this bound to be tight. This is joint work with Louwe B. Kuijer, Patrick Totzke and Martin Zimmermann.