Overview
- Authors:
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Stephen L. Bloom
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Department of Computer Science, Stevens Institute of Technology, Hoboken, USA
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Zoltán Ésik
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Department of Computer Science, A. József University, Szeged, Hungary
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About this book
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.
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Table of contents (15 chapters)
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- Stephen L. Bloom, Zoltán Ésik
Pages 1-6
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- Stephen L. Bloom, Zoltán Ésik
Pages 7-21
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- Stephen L. Bloom, Zoltán Ésik
Pages 23-45
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- Stephen L. Bloom, Zoltán Ésik
Pages 47-92
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- Stephen L. Bloom, Zoltán Ésik
Pages 93-111
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- Stephen L. Bloom, Zoltán Ésik
Pages 113-158
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- Stephen L. Bloom, Zoltán Ésik
Pages 159-213
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- Stephen L. Bloom, Zoltán Ésik
Pages 215-241
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- Stephen L. Bloom, Zoltán Ésik
Pages 243-288
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- Stephen L. Bloom, Zoltán Ésik
Pages 289-351
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- Stephen L. Bloom, Zoltán Ésik
Pages 353-447
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- Stephen L. Bloom, Zoltán Ésik
Pages 449-480
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- Stephen L. Bloom, Zoltán Ésik
Pages 481-511
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- Stephen L. Bloom, Zoltán Ésik
Pages 513-549
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- Stephen L. Bloom, Zoltán Ésik
Pages 551-611
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Back Matter
Pages 612-632
Authors and Affiliations
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Department of Computer Science, Stevens Institute of Technology, Hoboken, USA
Stephen L. Bloom
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Department of Computer Science, A. József University, Szeged, Hungary
Zoltán Ésik