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 author       = "Andr{\'e} Arnold",
 year         = "1999",
 title        = "The $\mu $-calculus alternation-depth hierarchy is strict on binary trees",
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 volume       = "33",
 number       = "4/5",
 pages        = "329--340",
 url          = "http://dx.doi.org/10.1051/ita:1999121",
)
@incollection(FixedPointTrees_AN92,
 author       = "Andr{\'e} Arnold and Damian Niwi\'nski",
 year         = "1992",
 title        = "Fixed point characterization of weak monadic logic definable sets of trees",
 booktitle    = "Tree Automata and Languages",
 pages        = "159--188",
)
@misc(bilkowski_personal2010,
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 year         = "2010",
 howpublished = "personal communication",
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 year         = "2006",
 title        = "Bounds in $\omega $-Regularity",
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 pages        = "285--296",
 url          = "http://doi.ieeecomputersociety.org/10.1109/LICS.2006.17",
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 author       = "Julian C. Bradfield",
 year         = "1999",
 title        = "Fixpoint alternation: {A}rithmetic, transition systems, and the binary tree",
 journal      = "ITA",
 volume       = "33",
 number       = "4/5",
 pages        = "341--356",
 url          = "http://dx.doi.org/10.1051/ita:1999122",
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 author       = "Arnaud Carayol and Christof L{\"o}ding",
 year         = "2007",
 title        = "{MSO} on the Infinite Binary Tree: Choice and Order",
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 pages        = "161--176",
 url          = "http://dx.doi.org/10.1007/978-3-540-74915-8_15",
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 title        = "Choice functions and well-orderings over the infinite binary tree",
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 author       = "Damian Niwi\'nski",
 year         = "1986",
 title        = "On Fixed-Point Clones (Extended Abstract)",
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@unpublished(unambiguous_unpublished,
 author       = "Damian Niwi\'nski and Igor Walukiewicz",
 year         = "1996",
 title        = "Ambiguity problem for automata on infinite trees",
 note         = "Unpublished note",
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@article(gap,
 author       = "Damian Niwi\'nski and Igor Walukiewicz",
 year         = "2003",
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 pages        = "1--23",
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 author       = "Michael O. Rabin",
 year         = "1970",
 title        = "Weakly Definable Relations and Special Automata",
 journal      = "Mathematical Logic and Foundations of Set Theory",
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