  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.
