Robust Computation Tree Logic

TL;DR

This paper introduces robust versions of CTL and CTL* with multi-valued semantics to quantify and handle small violations in system specifications, enhancing their expressiveness without increasing computational complexity.

Contribution

It develops robust extensions of CTL and CTL* using multi-valued semantics, demonstrating increased expressiveness and preserved computational complexity.

Findings

rCTL is more expressive than CTL.

rCTL* maintains the same expressiveness as CTL*.

Model checking, satisfiability, and synthesis complexities are unchanged.

Abstract

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 show that the model checking problem, the satisfiability problem, and the synthesis problem for rCTL and rCTL* have the same asymptotic complexity as their non-robust counterparts, implying that robustness can be added to branching-time logics for free.