Idempotency

ISBN: 9780521055383 出版年：1998 页码：457 Jeremy Gunawardena John M Taylor Michael Atiyah Cambridge University Press

The word idempotency siwfies the study of semirings in wmch the addition operation is idempotent: a + a = a. The best-mown example is the max-plus semiring, consisting of the real numbers with negative infinity adjoined in which addition is defined as max(a,b) and multiplication as a+b, the latter being distnbutive over the former. Interest in such structures arose in the late 1950s through the observation that certain problems of discrete optimisation could be linearised over suitable idempotent semirings. More recently the subject has established ~triguing connections with automata . theory, ~.hscrete e~ent syste~sl nonexpanSlVe mappmgs, nonlmear partla differential equations, optunisation theory and large deviations. TIle present paper was commissioned as an introduction to the volume of proceedings for the workshop on Idempotency held at Hewlett Packard's Basic Research Institute in the Mathematical Sciences (BRIMS) in October 1994. It aims to give an introductory survey, from a coherent mathematical viewpoin1 of the recent developments in the subject. iDe major open problems are pointed out and an extensive bibliography is provided.