Pacing Types for Asynchronous Stream Equations

2026-05-26

AI Summary

This work addresses the inconsistency in synchronization strategies arising from heterogeneous sensor sampling rates in asynchronous data stream monitoring by introducing a novel tempo type system for the RTLola language. By formally capturing the semantics of tempo annotations and integrating type-theoretic principles with machine-checked proofs in Coq, the system enables, for the first time, static verification of synchronization consistency across asynchronous streams. We develop this type system over a core fragment of RTLola and provide a machine-verified proof of its soundness, guaranteeing that users cannot express unrealizable synchronization logic. This ensures the temporal correctness of generated monitors, thereby enhancing the reliability of runtime verification in asynchronous settings.

Abstract

Stream-based monitoring is a runtime verification approach where a monitor aggregates streams of input data from sensors and other sources to give real-time statistics and assessments of a system's health. One of the central challenges in designing reliable stream-based monitors is to deal with the asynchronous nature of data streams: in concrete applications, the different sensors being monitored produce values at different speeds, and it is the monitor's responsibility to correctly react to the asynchronous arrival of different streams of values. To ease this process, modern frameworks for stream-based monitoring such as RTLola enable users to finely specify data synchronization policies via a system of pacing annotations. While this feature simplifies the design of monitors, it can also lead users to write inconsistent policies, where synchronization between two streams is explicitly requested via annotations, but cannot always be achieved. To mitigate this issue, this paper presents pacing types, a novel type system implemented in RTLola to ensure that monitors for asynchronous streams are free of timing inconsistencies. We give a formal semantics to pacing annotations for a core fragment of RTLola, and present a soundness proof of the pacing type system. For an additional level of guarantees, we machine-checked the soundness proof using the Rocq proof assistant.

Problem

• asynchronous streams
• stream-based monitoring
• synchronization policies
• timing inconsistencies
• pacing annotations

Innovation

• pacing types
• asynchronous stream monitoring
• type system
• RTLola
• formal verification