Partial Correctness of GCD Algorithm

Ievgen Ivanov 1 , Artur Korniłowicz 2 , and Mykola Nikitchenko 3
  • 1 Taras Shevchenko National University, , Kyiv, Ukraine
  • 2 Institute of Informatics, University of Białystok,, Poland
  • 3 Taras Shevchenko National University, , Kyiv, Ukraine

Summary

In this paper we present a formalization in the Mizar system , ] 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 , .

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

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