License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2020.20
URN: urn:nbn:de:0030-drops-116633
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11663/
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Ferrère, Thomas ; Henzinger, Thomas A. ; Kragl, Bernhard

Monitoring Event Frequencies

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LIPIcs-CSL-2020-20.pdf (0.6 MB)

Abstract

The monitoring of event frequencies can be used to recognize behavioral anomalies, to identify trends, and to deduce or discard hypotheses about the underlying system. For example, the performance of a web server may be monitored based on the ratio of the total count of requests from the least and most active clients. Exact frequency monitoring, however, can be prohibitively expensive; in the above example it would require as many counters as there are clients. In this paper, we propose the efficient probabilistic monitoring of common frequency properties, including the mode (i.e., the most common event) and the median of an event sequence. We define a logic to express composite frequency properties as a combination of atomic frequency properties. Our main contribution is an algorithm that, under suitable probabilistic assumptions, can be used to monitor these important frequency properties with four counters, independent of the number of different events. Our algorithm samples longer and longer subwords of an infinite event sequence. We prove the almost-sure convergence of our algorithm by generalizing ergodic theory from increasing-length prefixes to increasing-length subwords of an infinite sequence. A similar algorithm could be used to learn a connected Markov chain of a given structure from observing its outputs, to arbitrary precision, for a given confidence.

BibTeX - Entry

@InProceedings{ferrre_et_al:LIPIcs:2020:11663,
  author =	{Thomas Ferr{\`e}re and Thomas A. Henzinger and Bernhard Kragl},
  title =	{{Monitoring Event Frequencies}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11663},
  URN =		{urn:nbn:de:0030-drops-116633},
  doi =		{10.4230/LIPIcs.CSL.2020.20},
  annote =	{Keywords: monitoring, frequency property, Markov chain}
}

Keywords: monitoring, frequency property, Markov chain
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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