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Implementation of Interval Arithmetic in CORA 2016

15 pagesPublished: February 1, 2017

Abstract

Interval arithmetic can be seen as one of the workhorses for formal verification approaches. The popularity of interval arithmetic stems form the fact that the possible outcomes of almost all frequently occurring mathematical expressions can be bounded. A disadvantage of interval arithmetic is that due to the negligence of dependencies of variables in expressions, results can be overly conservative. For this reason, interval arithmetic is typically used in formal verification tools when formulas are not contributing much to the accuracy of the overall approach, but do not belong to a restrictive class of expressions and are thus hard to evaluate. Although a lot of textbooks and software manuals for interval arithmetic exist, we have not found a complete and detailed description of how all standard mathematical functions are evaluated. This work changes this situation and describes concisely the evaluation of all standard mathematical functions. The described techniques are implemented as a class in CORA, a free MATLAB tool for continuous reachability analysis. Previously, CORA used the MATLAB toolbox INTLAB, but this tool is no longer freely available. Thus, our interval arithmetic class is currently the only freely available implementation of interval arithmetic that runs under current MATLAB versions. We have thoroughly tested our implementation against INTLAB and present the results.

Keyphrases: CORA, hybrid systems, interval arithmetic, MATLAB, reachability, tool

In: Goran Frehse and Matthias Althoff (editors). ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems, vol 43, pages 91--105

Links:
BibTeX entry
@inproceedings{ARCH16:Implementation_of_Interval_Arithmetic,
  author    = {Matthias Althoff and Dmitry Grebenyuk},
  title     = {Implementation of Interval Arithmetic in CORA 2016},
  booktitle = {ARCH16. 3rd International Workshop on Applied Verification for Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {43},
  pages     = {91--105},
  year      = {2017},
  publisher = {EasyChair},
  bibsource = {EasyChair, http://www.easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/ZRJ},
  doi       = {10.29007/w19b}}
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