Predicate abstraction for hyperliveness verification

Temporal hyperproperties are system properties that relate multiple execution traces. In finite-state systems, temporal hyperproperties are supported by model-checking algorithms, and tools for general temporal logics like HyperLTL exist. In infinite-state systems, the analysis of temporal hyperproperties has, so far, been limited to k-safety properties, i.e., properties that stipulate the absence of a bad interaction between any k traces. In this paper, we present an automated method for the verification of ${\forall }^k{\exists }^l$ -safety properties in infinite-state systems. A ${\forall }^k{\exists }^l$ -safety property stipulates that for any k traces, there exist l traces such that the resulting $k+l$ traces do not interact badly. This combination of universal and existential quantification captures many properties beyond k-safety, including hyperliveness properties such as generalized non-interference or program refinement. Our verification method is based on a strategy-based instantiation of existential trace quantification combined with a program reduction, both in the context of a fixed predicate abstraction.