On the formalization of the notion of a concurrent algorithm
Abstract
Previous papers give accounts of quests for satisfactory formalizations of the classical informal notion of an algorithm and the contemporary informal notion of an interactive algoritm. In this paper, an attempt is made to generalize the results of the former quest to the contemporary informal notion of a concurrent algorithm. The notion of a concurrent proto-algorithm is introduced. The thought is that concurrent algorithms are equivalence classes of concurrent proto-algorithms under an appropriate equivalence relation. Three equivalence relations are defined. Two of them are deemed to be bounds for an appropriate equivalence relation and the third is likely an appropriate one. The connection between concurrency and non-determinism in the presented setting is also addressed.
Cite
@article{arxiv.2410.17821,
title = {On the formalization of the notion of a concurrent algorithm},
author = {C. A. Middelburg},
journal= {arXiv preprint arXiv:2410.17821},
year = {2026}
}
Comments
20 pages. It has recently been discovered that the serious flaws that led to the withdrawal of version 1 in March 2025 can, surprisingly enough, be repaired by minor changes to the definitions of the algorithmic and computational step functions and to the proof of Theorem 3