The Power of Spreadsheet Computations

TL;DR

This paper explores the computational capabilities of spreadsheets with formulas, analyzing how their structure and size relate to classical parallel computation models and complexity classes.

Contribution

It establishes a formal connection between spreadsheet dimensions, reference structures, and parallel complexity classes, introducing universal spreadsheets and complexity insights.

Findings

Spreadsheet classes correspond to parallel complexity classes.

Universal spreadsheets can emulate other spreadsheets in their class.

Some spreadsheet classes can encode polynomial-time complete problems.

Abstract

We investigate the expressive power of spreadsheets. We consider spreadsheets which contain only formulas, and assume that they are small templates, which can be filled to a larger area of the grid to process input data of variable size. Therefore we can compare them to well-known machine models of computation. We consider a number of classes of spreadsheets defined by restrictions on their reference structure. Two of the classes correspond closely to parallel complexity classes: we prove a direct correspondence between the dimensions of the spreadsheet and amount of hardware and time used by a parallel computer to compute the same function. As a tool, we produce spreadsheets which are universal in these classes, i.e. can emulate any other spreadsheet from them. In other cases we implement in the spreadsheets in question instances of a polynomial-time complete problem, which indicates that the the spreadsheets are unlikely to have efficient parallel evaluation algorithms. Thus we get a picture how the computational power of spreadsheets depends on their dimensions and structure of references.