The Complexity of Comparative Text Analysis -- "The Gardener is always the Murderer" says the Fourth Machine

TL;DR

This paper explores the mathematical and computational complexity of comparative text analysis, proposing a Boolean ring framework to better understand the limitations and structures involved in automated text comparison.

Contribution

It introduces a novel algebraic approach using Boolean rings to model the comparison process in text analysis, analyzing its computational complexity.

Findings

Comparison operations form a Boolean ring structure.

The algebraic framework reveals inherent computational complexity.

Provides a foundation for future complexity analysis of text comparison algorithms.

Abstract

There is a heated debate about how far computers can map the complexity of text analysis compared to the abilities of the whole team of human researchers. A "deep" analysis of a given text is still beyond the possibilities of modern computers. In the heart of the existing computational text analysis algorithms there are operations with real numbers, such as additions and multiplications according to the rules of algebraic fields. However, the process of "comparing" has a very precise mathematical structure, which is different from the structure of an algebraic field. The mathematical structure of "comparing" can be expressed by using Boolean rings. We build on this structure and define the corresponding algebraic equations lifting algorithms of comparative text analysis onto the "correct" algebraic basis. From this point of view, we can investigate the question of {\em computational} complexity of comparative text analysis.