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

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 33, Issue: 4-5, page 341-356
- ISSN: 0988-3754

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topBradfield, J. C.. "Fixpoint alternation: arithmetic, transition systems, and the binary tree." RAIRO - Theoretical Informatics and Applications 33.4-5 (2010): 341-356. <http://eudml.org/doc/221964>.

@article{Bradfield2010,

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.
},

author = {Bradfield, J. C.},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Fixpoints; mu-calculus; alternation; modal logic.; modal mu-calculus alternation hierarchy},

language = {eng},

month = {3},

number = {4-5},

pages = {341-356},

publisher = {EDP Sciences},

title = {Fixpoint alternation: arithmetic, transition systems, and the binary tree},

url = {http://eudml.org/doc/221964},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Bradfield, J. C.

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

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 4-5

SP - 341

EP - 356

AB -
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.

LA - eng

KW - Fixpoints; mu-calculus; alternation; modal logic.; modal mu-calculus alternation hierarchy

UR - http://eudml.org/doc/221964

ER -

## References

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- D. Niwinski, On fixed point clones, L. Kott, Ed., in Proc. 13th ICALP. Springer, Berlin, Lecture Notes in Comput. Sci.226 (1986) 464-473. Zbl0596.68036
- D. Niwinski, Fixed point characterization of infinite behavior of finite state systems. Theoret. Comput. Sci.189 (1997) 1-69. Zbl0893.68102
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