research-article

Computing the Skorokhod distance between polygonal traces

Authors:

Rupak Majumdar,

Vinayak S. PrabhuAuthors Info & Claims

HSCC '15: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

Pages 199 - 208

https://doi.org/10.1145/2728606.2728618

Published: 14 April 2015 Publication History

Abstract

The Skorokhod distance is a natural metric on traces of continuous and hybrid systems. It measures the best match between two traces, each mapping a time interval [0, T] to a metric space O, when continuous bijective timing distortions are allowed. Formally, it computes the infimum, over all timing distortions, of the maximum of two components: the first component quantifies the timing discrepancy of the timing distortion, and the second quantifies the mismatch (in the metric space O) of the values after the timing distortion. Skorokhod distances appear in various fundamental hybrid systems analysis concerns: from definitions of hybrid systems semantics and notions of equivalence, to practical problems such as checking the closeness of models or the quality of simulations. Despite its extensive use in semantics, the computation problem for the Skorokhod distance between two finite sampled-time hybrid traces remained open.

We address the problem of computing the Skorokhod distance between two polygonal traces (these traces arise when sampled-time traces are completed by linear interpolation between sample points). We provide an algorithm to compute the exact Skorokhod distance when trace values are compared using the L₁, L₂, and L_∞ norms in n dimensions. Our algorithm, based on a reduction to Fréchet distances, is fully polynomial-time, and incorporates novel polynomial-time procedures for a set of geometric primitives in IRⁿ over the three norms.

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Cited By

Helander SLaketa PIlmonen PNagy SVan Bever GViitasaari L(2022)Integrated shape-sensitive functional metricsJournal of Multivariate Analysis10.1016/j.jmva.2021.104880189:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.jmva.2021.104880
Roehm HOehlerking JWoehrle MAlthoff M(2019)Model Conformance for Cyber-Physical SystemsACM Transactions on Cyber-Physical Systems10.1145/33061573:3(1-26)Online publication date: 20-Aug-2019
https://dl.acm.org/doi/10.1145/3306157
Bernton EJacob PGerber MRobert C(2019)Approximate Bayesian computation with the Wasserstein distanceJournal of the Royal Statistical Society: Series B (Statistical Methodology)10.1111/rssb.1231281:2(235-269)Online publication date: 17-Feb-2019
https://doi.org/10.1111/rssb.12312
Show More Cited By

Index Terms

Computing the Skorokhod distance between polygonal traces
1. Computer systems organization
  1. Embedded and cyber-physical systems
  2. Real-time systems
2. Information systems
  1. Information systems applications
    1. Decision support systems
      1. Expert systems

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cover image ACM Conferences

HSCC '15: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

April 2015

321 pages

ISBN:9781450334334

DOI:10.1145/2728606

Program Chairs:
Antoine Girard
Université Joseph Fourier, Grenoble, France
,
Sriram Sankaranarayanan
University of Colorado at Boulder

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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IEEE-CSS: Control Systems Society
SIGBED: ACM Special Interest Group on Embedded Systems

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 April 2015

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FCT
Toyota Motors
Humboldt foundation

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HSCC '15

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IEEE-CSS
SIGBED

HSCC '15: 18th International Conference on Hybrid Systems: Computation and Control

April 14 - 16, 2015

Washington, Seattle

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Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Helander SLaketa PIlmonen PNagy SVan Bever GViitasaari L(2022)Integrated shape-sensitive functional metricsJournal of Multivariate Analysis10.1016/j.jmva.2021.104880189:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.jmva.2021.104880
Roehm HOehlerking JWoehrle MAlthoff M(2019)Model Conformance for Cyber-Physical SystemsACM Transactions on Cyber-Physical Systems10.1145/33061573:3(1-26)Online publication date: 20-Aug-2019
https://dl.acm.org/doi/10.1145/3306157
Bernton EJacob PGerber MRobert C(2019)Approximate Bayesian computation with the Wasserstein distanceJournal of the Royal Statistical Society: Series B (Statistical Methodology)10.1111/rssb.1231281:2(235-269)Online publication date: 17-Feb-2019
https://doi.org/10.1111/rssb.12312
Ratasich DPlatzer MGrosu RBartocci E(2019)Adaptive Fault Detection Exploiting Redundancy with Uncertainties in Space and Time2019 IEEE 13th International Conference on Self-Adaptive and Self-Organizing Systems (SASO)10.1109/SASO.2019.00013(23-32)Online publication date: Jun-2019
https://doi.org/10.1109/SASO.2019.00013
Lanotte RTini S(2019)Computing Bisimilarity Metrics for Probabilistic Timed AutomataIntegrated Formal Methods10.1007/978-3-030-34968-4_17(303-321)Online publication date: 22-Nov-2019
https://doi.org/10.1007/978-3-030-34968-4_17
Kido KSedwards SHasuo I(2019)Switching Delays and the Skorokhod Distance in Incrementally Stable Switched SystemsCyber Physical Systems. Design, Modeling, and Evaluation10.1007/978-3-030-17910-6_9(109-126)Online publication date: 13-Apr-2019
https://doi.org/10.1007/978-3-030-17910-6_9
Bartocci EDeshmukh JDonzé AFainekos GMaler ONičković DSankaranarayanan S(2018)Specification-Based Monitoring of Cyber-Physical Systems: A Survey on Theory, Tools and ApplicationsLectures on Runtime Verification10.1007/978-3-319-75632-5_5(135-175)Online publication date: 11-Feb-2018
https://doi.org/10.1007/978-3-319-75632-5_5
Deshmukh JMajumdar RPrabhu V(2017)Quantifying conformance using the Skorokhod metricFormal Methods in System Design10.1007/s10703-016-0261-850:2-3(168-206)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s10703-016-0261-8
Majumdar RPrabhu VAbate AFainekos G(2016)Computing Distances between Reach FlowpipesProceedings of the 19th International Conference on Hybrid Systems: Computation and Control10.1145/2883817.2883850(267-276)Online publication date: 11-Apr-2016
https://dl.acm.org/doi/10.1145/2883817.2883850
Majumdar R(2016)Robots at the Edge of the CloudProceedings of the 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems - Volume 963610.1007/978-3-662-49674-9_1(3-13)Online publication date: 2-Apr-2016
https://dl.acm.org/doi/10.1007/978-3-662-49674-9_1
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