Robust Computation Tree Logic

It is widely accepted that every system should be robust in that "small" violations of environment assumptions should lead to "small" violations of system guarantees, but it is less clear how to make this intuition mathematically precise. While significant efforts have been devoted to providing notions of robustness for Linear Temporal Logic (LTL), branching-time logics, such as Computation Tree Logic (CTL) and CTL*, have received less attention in this regard. To address this shortcoming, we develop "robust" extensions of CTL and CTL*, which we name robust CTL (rCTL) and robust CTL* (rCTL*). Both extensions are syntactically similar to their parent logics but employ multi-valued semantics to distinguish between "large" and "small" violations of the specification. We show that the multi-valued semantics of rCTL make it more expressive than CTL, while rCTL* is as expressive as CTL*. Moreover, we devise efficient model checking algorithms for rCTL and rCTL*, which have the same asymptotic time complexity as the model checking algorithms for CTL and CTL*, respectively.