Correspondence principle for idempotent calculus and some computer applications
Abstract
This paper is devoted to heuristic aspects of the socalled idempotent calculus. There is a correspondence between important, useful and interesting constructions and results over the field of real (or complex) numbers and similar constructions and results over idempotent semirings in the spirit of N. Bohr's correspondence principle in Quantum Mechanics. Some problems nonlinear in the traditional sense (for example, the Bellman equation and its generalizations) turn out to be linear over a suitable semiring; this linearity considerably simplifies the explicit construction of solutions. The theory is well advanced and includes, in particular, new integration theory, new linear algebra, spectral theory and functional analysis. It has a wide range of applications. Besides a survey of the subject, in this paper the correspondence principle is used to develop an approach to objectoriented software and hardware design for algorithms of idempotent calculus.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:math/0101021
 Bibcode:
 2001math......1021L
 Keywords:

 Mathematics  General Mathematics;
 06F05;
 16Y60;
 12K10;
 65K10
 EPrint:
 24 pages, no figures