Towards an Algebra of Computon Spaces

TL;DR

This paper introduces an algebraic framework for inductively composing spaces of computational constructs, enhancing the understanding of compositionality in complex systems beyond individual program composition.

Contribution

It proposes a novel algebraic model for composing spaces of sequential and parallel constructs, extending traditional program composition theories.

Findings

Defines an algebraic structure for compositional spaces

Provides semantics for the model

Demonstrates application with an abstract example

Abstract

Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since the inception of computer science. Unlike existing composition theories, this paper presents an algebraic model not for composing individual programs but for inductively composing spaces of sequential and/or parallel constructs. We particularly describe the semantics of the proposed model and present an abstract example to demonstrate its application.