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Implementation of Taylor models in CORA 2018

29 pagesPublished: September 17, 2018


Tool Presentation: Computing guaranteed bounds of function outputs when their input variables are bounded by intervals is an essential technique for many formal methods. Due to the importance of bounding function outputs, several techniques have been proposed for this problem, such as interval arithmetic, affine arithmetic, and Taylor models. While all methods provide guaranteed bounds, it is typically unknown to a formal verification tool which approach is best suitable for a given problem. For this reason, we present an implementation of the aforementioned techniques in our MATLAB tool CORA so that advantages and disadvantages of different techniques can be quickly explored without hav- ing to compile code. In this work we present the implementation of Taylor models and affine arithmetic; our interval arithmetic implementation has already been published. We evaluate the performance of our implementation using a set of benchmarks against Flow* and INTLAB. To the best of our knowledge, we have also evaluated for the first time how a combination of interval arithmetic and Taylor models performs: our results indicate that this combination is faster and more accurate than only using Taylor models.

Keyphrases: affine arithmetic, CORA, Flow*, interval arithmetic, INTLAB, rigorous function bounds, Taylor models

In: Goran Frehse (editor). ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems, vol 54, pages 145--173

BibTeX entry
  author    = {Matthias Althoff and Dmitry Grebenyuk and Niklas Kochdumper},
  title     = {Implementation of Taylor models in CORA 2018},
  booktitle = {ARCH18. 5th International Workshop on Applied Verification of Continuous and Hybrid Systems},
  editor    = {Goran Frehse},
  series    = {EPiC Series in Computing},
  volume    = {54},
  pages     = {145--173},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/zzc7}}
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