Linear, Geometric, and Structural Transformations

Le résumé fourni par la source

Every algorithm, however sophisticated, reduces to a nite sequence of elementary operations: additions, multiplications, comparisons. Every physical system that performs computation whether built from vacuum tubes, transistors, optical waveguides, or any substrate yet to be conceivedimplements those same operations through dierent physical means. What persists (underlies) all such changes of medium and representation is a layer of mathematical structure. This monograph is concerned with that layer, which remains invariant. The question that organizes the exposition is therefore what is being computed and what structural properties that object possesses independently of the coordinate system, basis, or hardware in which it happens to be expressed. This monograph began as an attempt to understand what remains invariant when formulas, coordinates, and representations are removed.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.