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Fixpoint alternation: arithmetic, transition systems, and the binary tree

Published online by Cambridge University Press:  15 August 2002

J. C. Bradfield
J. C. Bradfield*
Affiliation:
LFCS, Division of Informatics, University of Edinburgh, Edinburgh EH9 3JZ, U.K., jcb@lfcs.ed.ac.uk. BRICS, Department of Computer Science, Aarhus University, Bygning 540, Ny Munkegade, 8000 Århus C, Denmark.
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Abstract

We provide an elementary proof of the fixpoint alternation hierarchy in arithmetic, which in turn allows us to simplify the proof of the modal mu-calculus alternation hierarchy. We further show that the alternation hierarchy on the binary tree is strict, resolving a problem of Niwiński.

Keywords

Fixpointsmu-calculusalternationmodal logic.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 4-5 , July 1999 , pp. 341 - 356
Copyright
© EDP Sciences, 1999

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References

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