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Automata Logics, and Infinite Games pp 359–364Cite as

Some Fixed Point Basics

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2500))

Abstract

This chapter is intended to give the reader a brief overview of some basic notations and theorems regarding fixed points of monotone functions on complete lattices. The main results stated and proved here are the Knaster-Tarski Theorem [175] (Theorem 20.4), and Theorem 20.12 on the characterization of simultaneous fixed points. That is, this chapter provides proofs and some additional insights to propositions introduced in Chapter 10.

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Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität zu, Kiel

    Carsten Fritz

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  1. Carsten Fritz
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Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Universität Kiel, Christian-Albrechts-Platz 4, 24118, Kiel, Germany

    Thomas Wilke

  2. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  3. Lehrstuhl Informatik VII, RWTH Aachen, 52056, Aachen, Germany

    Wolfgang Thomas

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© 2002 Springer-Verlag Berlin Heidelberg

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Fritz, C. (2002). Some Fixed Point Basics. In: Grädel, E., Thomas, W., Wilke, T. (eds) Automata Logics, and Infinite Games. Lecture Notes in Computer Science, vol 2500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36387-4_20

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  • DOI: https://doi.org/10.1007/3-540-36387-4_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00388-5

  • Online ISBN: 978-3-540-36387-3

  • eBook Packages: Springer Book Archive

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