Robustness of Temporal Logic Specifications

Abstract

In this paper, we consider the robust interpretation of metric temporal logic (MTL) formulas over timed sequences of states. For systems whose states are equipped with nontrivial metrics, such as continuous, hybrid, or general metric transition systems, robustness is not only natural, but also a critical measure of system performance. In this paper, we define robust, multi-valued semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, e, from unsatisfiability. We prove that any other timed trace which remains e-close to the initial one also satisfies the same MTL specification with the usual Boolean semantics. We derive a computational procedure for determining an under-approximation to the robustness degree e of the specification with respect to a given finite timed state sequence. Our approach can be used for robust system simulation and testing, as well as form the basis for simulation-based verification.