Monitoring extended hypernode logic

Hypernode logic can reason about the prefix relation on stutter-reduced finite traces through the stutter-reduced prefix predicate. We increase the expressiveness of hypernode logic in two ways. First, we split the stutter-reduced prefix predicate into an explicit stutter-reduction operator and the classical prefix predicate on words. This change gives hypernode logic the ability to combine synchronous and asynchronous reasoning by explicitly stating which parts of traces can stutter. Second, we allow the use of regular expressions in formulas to reason about the structure of traces. This change enables hypernode logic to describe a mixture of trace properties and hyperproperties. We show how to translate extended hypernode logic formulas into multi-track automata, which are automata that read multiple input words. Then we describe a fully online monitoring algorithm for monitoring k-safety hyperproperties specified in the logic. We have implemented the monitoring algorithm, and evaluated it on monitoring synchronous and asynchronous versions of observational determinism, and on checking the privacy preservation by compiler optimizations.