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Numerical Verification of 10000-dimensional Linear Systems 10000x Faster

10 pagesPublished: September 17, 2018

Abstract

Tool Presentation: We evaluate an improved reachability algorithm for linear (and affine) systems implemented in the continuous branch of the Hylaa tool. While Hylaa’s earlier approach required n simulations to verify an n-dimensional system, the new method takes advantage of additional problem structure to produce the same verification result in significantly less time. If the initial states can be defined in i dimensions, and the output variables related to the property being checked are o-dimensional, the new approach needs only min(i,o) simulations to verify the system, or produce a counter-example. In addition to reducing the number of simulations, a second improvement speeds up individual simulations when the dynamics is sparse by using Krylov subspace methods.
At ARCH 2017, we used the original approach to verify nine large linear benchmarks taken from model order reduction. Here, we run the new algorithm on the same set of benchmarks, and get an identical verification result in a fraction of the time. None of the benchmarks need more than tens of seconds to complete. The largest system with 10922 dimensions, which took over 24 hours using last year’s method, is verified in 3.4 seconds.

Keyphrases: counter-example generation, Hylaa, linear systems, reachability analysis, verification

In: Goran Frehse (editor). ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 54, pages 135--144

Links:
BibTeX entry
@inproceedings{ARCH18:Numerical_Verification_of_10000_dimensional,
  author    = {Stanley Bak},
  title     = {Numerical Verification of 10000-dimensional Linear Systems 10000x Faster},
  booktitle = {ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems},
  editor    = {Goran Frehse},
  series    = {EPiC Series in Computing},
  volume    = {54},
  pages     = {135--144},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/Hzw2},
  doi       = {10.29007/gv5q}}
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