Signal Convolution Logic

Abstract

We introduce a new logic called Signal Convolution Logic (SCL) that combines temporal logic with convolutional filters from digital signal processing. SCL enables to reason about the percentage of time a formula is satisfied in a bounded interval. We demonstrate that this new logic is a suitable formalism to effectively express non-functional requirements in Cyber-Physical Systems displaying noisy and irregular behaviours. We define both a qualitative and quantitative semantics for it, providing an efficient monitoring procedure. Finally, we prove SCL at work to monitor the artificial pancreas controllers that are employed to automate the delivery of insulin for patients with type-1 diabetes.

Control Synthesis using Signal Temporal Logic Specifications with Integral and Derivative Predicates

“…Therefore, the conventional robustness degree cannot differentiate between such cases and cannot provide comprehensive information about the signals x and x ′ . To address this issue, [13]- [15] define new measures that can capture the duration of predicate satisfaction. While existing metrics can track how long a predicate x(t) ≥ δ is satisfied within an interval [0, T ], they are not able to address a notion of cumulative success such as…”

“…Nonlinear systems can be linearized around known equilibrium points. Furthermore, the mission constraints can be encoded as linear inequalities with binary variables as in ( 13), ( 14), (15). Accordingly, under linear dynamics and predicates, the constrained optimization problem in (12) can be posed as a mixed-integer linear program.…”

“…For example, since conventional robustness degree focuses on critical time instants, authors of [13] and [14] define new measures to differentiate the satisfaction of predicates achieved at multiple time instants from the instantaneous satisfaction of them. With a similar motivation, a temporal operator is defined in [15] that explicitly specifies how long a predicate must be satisfied. However, existing approaches do not accommodate predicates expressing cumulative success or local behavior A.T. Buyukkocak and D. Aksaray are with the Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, buyuk012@umn.edu, daksaray@umn.edu, and Y.…”

Specification and Efficient Monitoring Beyond STL

“…An alternative direction is to define a quantifier-free specification language with more flexible syntax and sliding window operations. For example, Signal Convolution Logic (SCL [20]) allows to specify properties using convolution with a set of select kernels. In particular, it can express properties of the form "statement ϕ holds on an interval for at least X% of the time".…”

“…We offer a version of "until" operator that performs aggregation over a sliding window of dynamic width, that depends on satisfaction of some formula. This distinguishes us from the works that focus on aggregation over a fixed window [20].…”