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Iteration Theories of Boolean Functions

  • Zoltán Ésik
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Boolean Function Monotonic Function Point Identity Complete Lattice Point Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    H. Bekić, Definable operations in general algebras, and the theory of automata and flowcharts, Technical Report, IBM Laboratory, Vienna, 1969.Google Scholar
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    S. L. Bloom and Z. Ésik, Iteration Theories: The Equational Logic of Iterative Processes, Springer, 1993.Google Scholar
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    S. L. Bloom and Z. Ésik, There is no finite axiomatization of iteration theories, in: proc. LATIN 2000, LNCS 1776, Springer, 2000, 367–376.Google Scholar
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    E. L. Post, The Two-Valued Iterative Systems of Mathematical Logic, Princeton University Press, 1941.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Zoltán Ésik
    • 1
  1. 1.Department of Computer ScienceUniversity of SzegedSzegedHungary

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