Software Verification of Hyperproperties Beyond k-Safety

Temporal hyperproperties are system properties that relate multiple execution traces. For (finite-state) hardware, temporal hyperproperties are supported by model checking algorithms, and tools for general temporal logics like HyperLTL exist. For (infinite-state) software, 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 allows us to express many properties beyond $k$-safety, including, for example, generalized non-interference or program refinement. Our 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. Importantly, our framework allows for mutual dependence of strategy and reduction.