📝 SummarXiv

Abstract

HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, i.e., properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking. Here, we settle the complexity of satisfiability for HyperQPTL as well as satisfiability, finite-state satisfiability, and model-checking for HyperQPTL$^+$: the former is $\Sigma^2_1$-complete, the latter are all equivalent to truth in third-order arithmetic, i.e., all four are very undecidable.