Correspondence principle for idempotent calculus and some computer applications

• DOI: 10.48550/arxiv.math/0101021
• Publication Date: 2001-01-01
• Authors: Grigori Litvinov; V. P. Maslov
• Keywords: General Mathematics (math.GM); 0202 electrical engineering, electronic engineering, information engineering; FOS: Mathematics; 02 engineering and technology; 06F05, 16Y60, 12K10, 65K10; 0101 mathematics; Mathematics - General Mathematics; 01 natural sciences

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