Relaxations of associativity and preassociativity for variadic functions

TL;DR

This paper introduces parameterized relaxations of associativity and preassociativity for variadic functions, providing factorization characterizations, natural hierarchies, and potential applications in data and language processing.

Contribution

It proposes new parameterized notions of associativity and preassociativity, along with their factorization-based descriptions and hierarchy structures.

Findings

Hierarchies of functions based on relaxed properties

Factorization results characterizing the relaxations

Potential applications in measuring degrees of associativeness

Abstract

In this paper we consider two properties of variadic functions, namely associativity and preassociativity, that are pertaining to several data and language processing tasks. We propose parameterized relaxations of these properties and provide their descriptions in terms of factorization results. We also give an example where these parameterized notions give rise to natural hierarchies of functions and indicate their potential use in measuring the degrees of associativeness and preassociativeness. We illustrate these results by several examples and constructions and discuss some open problems that lead to further directions of research.