Abstract State Machines with Exact Real Arithmetic

Abstract

Type-2 Theory of Effectivity is a well established theory of computability on infinite strings, which in this paper is exploited to define a data type ( Real ) as part of the background structure of Abstract State Machines. Real numbers are represented by rapidly converging Cauchy sequences, on top of which standard operations such as addition, multiplication, division, exponentials, trigonometric functions, etc. can be defined. In this way exact computation with real numbers is enabled. Output can be generated at any degree of precision by exploring only sufficiently long prefixes of the representing Cauchy sequences.

Document

If you cannot see the document below, the PDF document is most likely not freely accessible. In this case, please try to access the document via this link.

Reference

% BibTex
@inproceedings{BeierleS18,
  author       = {Christoph Beierle and
                  Klaus{-}Dieter Schewe},
  editor       = {Michael J. Butler and
                  Alexander Raschke and
                  Thai Son Hoang and
                  Klaus Reichl},
  title        = {Abstract State Machines with Exact Real Arithmetic},
  booktitle    = {Abstract State Machines, Alloy, B, TLA, VDM, and {Z} - 6th International
                  Conference, {ABZ} 2018, Southampton, UK, June 5-8, 2018, Proceedings},
  series       = {Lecture Notes in Computer Science},
  volume       = {10817},
  pages        = {139--154},
  publisher    = {Springer},
  year         = {2018},
  url          = {https://doi.org/10.1007/978-3-319-91271-4\_10},
  doi          = {10.1007/978-3-319-91271-4\_10},
  timestamp    = {Tue, 14 May 2019 10:00:50 +0200},
  biburl       = {https://dblp.org/rec/conf/asm/BeierleS18.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}