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2015 | OriginalPaper | Chapter

Robust Online Monitoring of Signal Temporal Logic

Authors : Jyotirmoy V. Deshmukh, Alexandre Donzé, Shromona Ghosh, Xiaoqing Jin, Garvit Juniwal, Sanjit A. Seshia

Published in: Runtime Verification

Publisher: Springer International Publishing

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Abstract

Requirements of cyberphysical systems (CPS) can be rigorously specified using Signal Temporal Logic (STL). STL comes equipped with semantics that are able to quantify how robustly a given signal satisfies an STL property. In a setting where signal values over the entire time horizon of interest are available, efficient algorithms for offline computation of the robust satisfaction value have been proposed. Only a few methods exist for the online setting, i.e., where only a partial signal trace is available and rest of the signal becomes available in increments (such as in a real system or during numerical simulations). In this paper, we formalize the semantics for robust online monitoring of partial signals using the notion of robust satisfaction intervals (\(\mathtt {RoSI}\)s). We propose an efficient algorithm to compute the \(\mathtt {RoSI}\) and demonstrate its usage on two real-world case studies from the automotive domain and massively-online CPS education. As online algorithms permit early termination when the satisfaction or violation of a property is found, we show that savings in computationally expensive simulations far outweigh any overheads incurred by the online approach.

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Footnotes
1
We omit the case of \(\mathbf {U}_I\) here for lack of space, although the rewriting approach of [7] can be adapted here and is implemented in our tool.
 
2
We remark that \(\varphi \) is equivalent to \(\Box _{[0,a]} \left( (y > 0) \implies \Diamond _{[b,c]}(x>0)\right) \), which is a common formula used to express a timed causal relation between two signals.
 
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Metadata
Title
Robust Online Monitoring of Signal Temporal Logic
Authors
Jyotirmoy V. Deshmukh
Alexandre Donzé
Shromona Ghosh
Xiaoqing Jin
Garvit Juniwal
Sanjit A. Seshia
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-23820-3_4

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