A theory of (linear-time) timed monitors

Abstract

Runtime Verification (RV) is gaining popularity due to its scalability and ability to analyse block-box systems. Monitoring is at the heart of RV; a logical formula ϕ, formalising some property of interest, is typically translated into a monitor that checks whether the system under scrutiny satisfies ϕ during its execution. A logical formula ϕ is violation (resp. satisfaction) monitorable iff there exists a monitor for ϕ that is both sound and complete w.r.t. its violation (resp. satisfaction). The monitorability problem is thus concerned with determining the largest subset of a logic L that is monitorable. Although this problem has been solved for expressive untimed logics, it remains open for timed logics, where formulae can express both the order of events and the quantity of time separating them. This paper solves the monitorability problem for Tlin, a new expressive (linear-time) timed µ-calculus that we propose. First, we show that Tlin is strictly more expressive than MTL, the de facto timed extension of LTL. Second, we identify MTlin, the largest monitorable fragment of Tlin: we characterise its largest subsets of formulae that are violation monitorable, satisfaction monitorable, and complete monitorable (both satisfaction and violation monitorable). To wit, this is the first work that answers the monitorability question for such an expressive timed logic.