Hyperhierarchy of Semantics - A Formal Framework for Hyperproperties Verification

Hyperproperties are becoming the, de facto, standard for reasoning about systems executions. They differ from classical trace properties since they are represented by sets of sets of executions instead of sets of executions. In this paper, we extend and lift the hierarchy of semantics developed in 2002 by P. Cousot in order to cope with verifica- tion of hyperproperties. In the standard hierarchy, semantics at different levels of abstraction are related with each other by abstract interpre- tation. In the same spirit, we propose an hyperhierarchy of semantics adding a new, more concrete, hyper level. The semantics defined at this hyper level are suitable for hyperproperties verification. Furthermore, all the semantics in the hyperhierarchy (the standard and the hyper ones) are still related by abstract interpretation.