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Fixpoint alternation: arithmetic, transition systems, and the binary tree
J. C. Bradfield
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 33 / Issue 4-5 / July 1999

Published online by Cambridge University Press:

15 August 2002, pp. 341-356

Print publication:

July 1999
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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.