Semirings and their Applications - Tapa blanda

This work is an updated and considerably expanded version of the author's book The Theory of Semirings, with Applications to Mathematics and Theoretical Science, which has been recognized as the definitive reference work in this area. This edition includes many of the new results in this area, as well as further applications of semiring theory in such areas as idempotent analysis, discrete dynamical systems, formal language theory, fuzzy set theory, optimization etc. The book contains an extensive bibliography and a large number of examples.

Audience: This book is aimed both at mathematicians and at researchers in applied mathematics and theoretical computer science. It is also suitable for use as a graduate-level textbook.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" [Golan, 1992], first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .