Time Robustness in MTL and Expressivity in Hybrid System Falsification

Abstract

Building on the work by Fainekos and Pappas and the one by Donzé and Maler, we introduce AvSTL, an extension of metric interval temporal logic by averaged temporal operators. Its expressivity in capturing both space and time robustness helps solving falsification problems (searching for a critical path in hybrid system models); it does so by communicating a designer's intention more faithfully to the stochastic optimization engine employed in a falsification solver. We also introduce a sliding window-like algorithm that keeps the cost of computing truth/robustness values tractable.[0,10] (v ≥ 80) ("the velocity reaches 80 km/h within 10 sec.") are 20 and 0, for the green and red signals on the right. Therefore space robustness is a "vertical margin" between a signal and a specification. An efficient algorithm is proposed in [11] for computing this notion of robustness.The notion of robustness is extended in [12] to take time robustness also into account. Consider the same specification [0,10] (v ≥ 80) against the green and red signals on the right. The green one is more robust since it reaches 80 km/h much earlier than the deadline (10 sec.), while the red one barely makes the deadline.The current work continues this line of work, with the slogan that expressivity of temporal logic should help falsification. With more expressivity, a designer's concerns

Metamathematics for Systems Design

“…Another example of such quantitative semantics is robustness semantics of temporal logics for continuous-time signals [3,24,26]. There the truth value of a formula u is a real number that designates how robustly the formula is satisfied.…”

“…a deadline specification is more robustly satisfied if the desired event occurs way in advance). The work [3] proposes to combine space and time robustness by suitable integration.…”

“…Also with the recent surge in advancement of techniques of machine learning and stochastic optimization, falsification by optimization attracts much attention as a scalable method for CPS quality assurance. We shall continue working on this topic, exploiting our expertise in logic (like in [3]) and also collaborating with machine learning and optimization techniques. A work related in essence is [31] for satisfiability check of assertions that involve floating-point operations.…”

Efficient Parametric Identification for STL

“…2. At the top of the figure, we show the input validity signal that talks about a single parameter p. It maps the interval [0, 3) to the set {v : v p ≥ 3}, [3,6) to {v : v p ≥ 2}, [6,9) to {v : v p ≥ 4}, [9,17) to {v : v p ≥ 3}, and [17,20) to {v : v p ≥ 0}. Below, we show the backward cones of these intervals w.r.t.…”

“…The combination is done with set union for the eventually operator and with set intersection for always. For a number of initial segments of d(φ, w), their backward cones start at time 0 (in the example in Fig.2, these are segments [0, 3), [3,6), and [6, 9)). We can produce the intermediate result of combining just these backward cones by scanning d(φ, w) backwards and computing the running union or intersection.…”