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Iteration Theories of Boolean Functions

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

A systematic study of the fixed point (or dagger) operation in Lawvere algebraic theories was initiated by Elgot and the ADJ group. Their work led to the introduction of iteration theories in 1980, which capture the equational properties of fixed points in the models proposed by Elgot and the ADJ group. The book [2] and the survey paper [3] provide ample evidence that the axioms of iteration theories have a general scope and constitute a complete description of the equational properties of the fixed point operation.

Partially supported by grant no. FKFP 247/1999 from the Ministry of Education of Hungary and grant no. T22423 from the National Foundation of Hungary for Scientific Research.

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References

  1. H. Bekić, Definable operations in general algebras, and the theory of automata and flowcharts, Technical Report, IBM Laboratory, Vienna, 1969.

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  2. S. L. Bloom and Z. Ésik, Iteration Theories: The Equational Logic of Iterative Processes, Springer, 1993.

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  3. S. L. Bloom and Z. Ésik, The equational logic of fixed points, Theoretical Computer Science, 179(1997), 1–60.

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  4. S. L. Bloom and Z. Ésik, There is no finite axiomatization of iteration theories, in: proc. LATIN 2000, LNCS 1776, Springer, 2000, 367–376.

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  5. J. W. de Bakker and D. Scott, A theory of programs. IBM, Vienna, 1969.

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  6. Z. Ésik, Group axioms for iteration, Information and Computation, 148(1999), 131–180.

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  7. D. Niwinski, Equational μ-calculus, Computation Theory, Zaborów, 1984, LNCS 208, Springer, 1985, 169–176.

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  8. E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Princeton University Press, 1941.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Szeged, P.O.B. 652, 6701, Szeged, Hungary

    Zoltán Ésik

Authors
  1. Zoltán Ésik
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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© 2000 Springer-Verlag Berlin Heidelberg

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Ésik, Z. (2000). Iteration Theories of Boolean Functions. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_30

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  • DOI: https://doi.org/10.1007/3-540-44612-5_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

  • eBook Packages: Springer Book Archive

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