Hyperproperties of real-valued signals

Abstract

A hyperproperty is a property that requires two or more execution traces to check. This is in contrast to properties expressed using temporal logics such as LTL, MTL and STL, which can be checked over individual traces. Hyperproperties are important as they are used to specify critical system performance objectives, such as those related to security, stochastic (or average) performance, and relationships between behaviors. We present the first study of hyperproperties of cyber-physical systems (CPSs). We introduce a new formalism for specifying a class of hyperproperties defined over real-valued signals, called HyperSTL. The proposed logic extends signal temporal logic (STL) by adding existential and universal trace quantifiers into STL's syntax to relate multiple execution traces. Several instances of hyperproperties of CPSs including stability, security, and safety are studied and expressed in terms of HyperSTL formulae. Furthermore, we propose a testing technique that allows us to check or falsify hyperproperties of CPS models. We present a discussion on the feasibility of falsifying or verifying various classes of hyperproperties for CPSs. We extend the quantitative semantics of STL to HyperSTL and show its utility in formulating algorithms for falsification of HyperSTL specifications. We demonstrate how we can specify and falsify HyperSTL properties for two case studies involving automotive control systems.