On the formalization of the notion of a concurrent algorithm

TL;DR

This paper explores formalizations of concurrent algorithms by introducing the concept of concurrent proto-algorithms and defining equivalence relations to classify them, linking concurrency with non-determinism.

Contribution

It generalizes previous formalizations of algorithms to the concurrent setting by defining concurrent proto-algorithms and their equivalence classes.

Findings

Defined three equivalence relations for concurrent proto-algorithms

Identified bounds for an appropriate equivalence relation

Connected concurrency with non-determinism in the formal setting

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.