The correspondence principle for idempotent calculus and some computer applications. (English) Zbl 0897.68050

Gunawardena, Jeremy (ed.), Idempotency. Based on a workshop, Bristol, UK, October 3–7, 1994, Cambridge: Cambridge University Press. 420-443 (1998).
Summary: This paper is devoted to heuristic aspects of the so-called 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. Idempotent analogs for some basic ideas, constructions and results in functional analysis and mathematical physics are discussed from this point of view. Thus the correspondence principle is a powerful heuristic tool to apply unexpected analogies and ideas borrowed from different areas of mathematics and theoretical physics.
In this paper, the correspondence principle is used to develop an approach to object-oriented software and hardware design for algorithms of idempotent calculus and scientific calculations. In particular, there is a regular method for constructing back-end processors and technical devices intended for an implementation of basic algorithms of idempotent calculus and mathematics of semirings. These hardware facilities increase the speed of data processing. Moreover, this approach is useful for software and hardware design in the general case of algorithms which are not “idempotent”.
For the entire collection see [Zbl 0882.00035].


68W10 Parallel algorithms in computer science
68W30 Symbolic computation and algebraic computation
20M99 Semigroups
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