Year: 2023
Type: preprint
Abstract: Our main result is a new proof of correctness of Euclid's algorithm. The proof is conducted in algorithmic theory of natural numbers Th3. A formula H is constructed that expresses the halting property of the algorithm. Next, the proof of H is is presented. In the proof we make use of inference rules of calculus of programs. The only formulas accepted without the proof are axioms of program calculus or axioms of the theory Th3. We complete our result by showing that the theorem on correctness of Euclid's algorithm can not be proved in any elementary theory of natural numbers.
Source: arXiv (Cornell University)
Author: Salwicki, Andrzej
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4388444929