Iteration Theories: The Equational Logic of Iterative Processes (Monographs in Theoretical Computer Science. An EATCS Series)

Bloom, Stephen L.; Esik, Zoltan

ISBN 10: 3540563784 / ISBN 13: 9783540563785

Published by Springer, 1993

About this Item

Page block firm and clean, binding unblemished, boards straight, no markings of any kind. Fine, like new condition. Well packaged and promptly shipped from California. Partnered with Friends of the Library since 2010.

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Bibliographic Details

• Title: Iteration Theories: The Equational Logic of Iterative Processes (Monographs in Theoretical Computer Science. An EATCS Series)
• Publisher: Springer
• Publication Date: 1993
• Language: English
• ISBN 10: 3540563784
• ISBN 13: 9783540563785
• Binding: Hardcover
• Condition: LikeNew

About this title

Synopsis

This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au- dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi- nary facts in Chapter 1. Written both for graduate students and research scientists in theoret- ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap- tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in- finitary regular languages, trees, synchronization trees, 2-categories, and others.

Synopsis

Written both for graduate students and research scientists in theoretical computer science and mathematics, this book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantic models, the equational properties of the fixed point operation are captured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and infinitary regular languages, trees, synchronization trees, 2-categories, and others. The book begins with a gentle introduction to the study of universal algebra in the framework of algebraic theories. A useful calculus is developed for manipulating algebraic theory terms.

The reader is then guided through a vast terrain of theorems and applications by means of detailed proofs, examples and exercises, with the emphasis on equational proofs. The last chapter shows that the familiar topic of correctness logic is a special case of the equational logic of iteration theories. Several significant open problems are scattered throughout the text.