Complexity of term representations of finitary functions

TL;DR

This paper investigates the complexity of representing finitary functions through terms in algebraic structures, focusing on bounds for term length and height, and their robustness across different basic operations.

Contribution

It provides bounds for the length and height of terms representing functions and shows these bounds are often stable under changes in the structure's basic operations.

Findings

Bounds for term length and height are established.

Robustness of these bounds against operation changes is demonstrated.

Implications for algebraic complexity and structure analysis.

Abstract

The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. We consider bounds for the length and the height of the terms expressing these functions, and we show that these bounds are often robust against the change of the basic operations of the structure.