Walid Taha
IDE, Halmstad University, Sweden and Computer Science, Rice University, USA
Robert Cartwright
Computer Science, Rice University, USA and IDE, Halmstad University, Sweden
Download article
http://dx.doi.org/10.3384/ecp13090001Published in: Proceedings of the 4th Analytic Virtual Integration of Cyber-Physical Systems Workshop; December 3; Vancouver; Canada
Linköping Electronic Conference Proceedings 90:1, p. 1-4
Published: 2013-11-13
ISBN: 978-91-7519-451-6
ISSN: 1650-3686 (print), 1650-3740 (online)
Comprehensive analytical modeling and simulation of cyberphysical systems is an integral part of the process that brings novel designs and products to life. But the effort needed to go from analytical models to running simulation code can impede or derail this process. Our thesis is that this process is amenable to automation; and that automating it will accelerate the pace of innovation. This paper reviews some basic concepts that we found interesting or thought-provoking; and articulates some questions that may help prove or disprove this thesis. While based on ideas drawn from different disciplines outside programming languages; we observe that all these questions pertain in a profound way to how we need to reason and compute with real numbers.
[1] Richard Beals. Analysis: An Introduction. Cambridge University Press; 2004. doi: doi:
10.1017/CBO9780511755163
[2] H. Boehm; R. Cartwright; M. J. O’Donnell; and M. Riggle. Exact Real Arithmetic: A Case Study in Higher Order Programming. In Proceedings of the 1986 Lisp and Functional Programming Conference; pages 162–173; 1986. doi: 10.1145/319838.319860
[3] L. E. J. Brouwer. Besitzt jede reelle zahl eine dezimalbruchentwicklung? Mathematische Annalen; 1991.
[4] Georg Cantor. Über eine eigenschaft des inbegriffes aller reellen algebraischen zahlen. Journal für die Reine und Angewandte Mathematik; 1874.
[5] Alexandre Chapoutot. Interval slopes as a numerical abstract domain for floating-point variables. In Static Analysis Symposium; 2010.
[6] Eric Goubault and Sylvie Putot. Under-approximations of computations in real numbers based on generalized affine arithmetic. In Static Analysis Symposium; 2007.
[7] Moore; Kearfott; and Cloud. Introduction to Interval Analysis. SIAM; 2009.
[8] N. T. Müller. The iRRAM: Exact arithmetic in C++. In Computability and Complexity in Analysis; 2001.
[9] Warwick Tucker. Validated Numerics: A Short Introduction to Rigorous Computations. Princton University Press; 2011.
[10] Angela Yun Zhu; Edwin Westbrook; Jun Inoue; Alexandre Chapoutot; Cherif Salama; Marisa Peralta; Travis Martin; Walid Taha; Marcia O’Malley; Robert Cartwright; Aaron Ames; and Raktim Bhattacharya. Mathematical equations as executable models of mechanical systems. In International Conference on Cyber-Physical Systems; 2010.
