Partial Correctness of GCD Algorithm

Ievgen Ivanov; Artur Korniłowicz; Mykola Nikitchenko

doi:10.2478/forma-2018-0014

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Partial Correctness of GCD Algorithm

Formalized Mathematics

Volume 26 (2018): Issue 2 (July 2018)

By: Ievgen Ivanov, Artur Korniłowicz and Mykola Nikitchenko

Open Access

|Dec 2018

Abstract

In this paper we present a formalization in the Mizar system [2, 1] of the correctness of the subtraction-based version of Euclid’s algorithm computing the greatest common divisor of natural numbers. The algorithm is written in terms of simple-named complex-valued nominative data [11, 4].

The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [7]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic with partial pre- and post-conditions [8, 10, 5, 3].

References

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2018-0014 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 165 - 173

Accepted on: Jun 29, 2018

Published on: Dec 24, 2018

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

greatest common divisor,

Related subjects:

Computer sciences, other

© 2018 Ievgen Ivanov, Artur Korniłowicz, Mykola Nikitchenko, published by University of Białystok
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 26 (2018): Issue 2 (July 2018)