The Complexity of Comparative Text Analysis -- "The Gardener is always the Murderer" says the Fourth Machine
This paper addresses a foundational problem in computational text analysis for researchers interested in the theoretical underpinnings and limitations of current algorithms, offering an incremental re-framing of the mathematical basis.
This paper re-evaluates computational text analysis by proposing that the mathematical structure of "comparing" text is better represented by Boolean rings rather than algebraic fields. By defining corresponding algebraic equations, the authors aim to investigate the computational complexity of comparative text analysis from this new foundation.
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.