@article(bradfield-strict,
 author       = {Julian C. Bradfield},
 year         = {1998},
 title        = {The modal mu-calculus alternation hierarchy is strict},
 journal      = {Theoretical Computer Science},
 volume       = {195},
 number       = {2},
 pages        = {133--153},
 doi          = {10.1016/S0304-3975(97)00217-X},
)
@article(bradfield1998simplifying,
 author       = {Julian C Bradfield},
 year         = {1999},
 title        = {Fixpoint alternation: Arithmetic, transition systems, and the binary tree},
 journal      = {RAIRO-Theoretical Informatics and Applications},
 volume       = {33},
 number       = {4-5},
 pages        = {341--356},
 doi          = {10.1051/ita:1999122},
)
@article(bradfield2007modal,
 author       = {Julian C. Bradfield and Colin Stirling},
 year         = {2007},
 title        = {Modal mu-calculi},
 journal      = {Handbook of modal logic},
 volume       = {3},
 pages        = {721--756},
 doi          = {10.1016/S1570-2464(07)80015-2},
)
@inproceedings(colcombet2013deciding,
 author       = {Thomas Colcombet and Denis Kuperberg and Christof L\"{o}ding and {Vanden Boom}, Michael},
 year         = {2013},
 title        = {{Deciding the weak definability of B\"{u}chi definable tree languages}},
 booktitle    = {{LIPIcs-Leibniz International Proceedings in Informatics}},
 volume       = {23},
 organization = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik},
 doi          = {10.4230/LIPIcs.CSL.2013.215},
)
@inproceedings(colcombet2008non,
 author       = {Thomas Colcombet and Christof L\"{o}ding},
 year         = {2008},
 title        = {{The non-deterministic Mostowski hierarchy and distance-parity automata}},
 booktitle    = {{International Colloquium on Automata, Languages, and Programming}},
 organization = {Springer},
 pages        = {398--409},
 doi          = {{10.1007/978-3-540-70583-3_33}},
)
@inproceedings(dawar2008,
 author       = {Anuj Dawar and Erich Gr{\"a}del},
 year         = {2008},
 title        = {The descriptive complexity of parity games},
 booktitle    = {International Workshop on Computer Science Logic},
 organization = {Springer},
 pages        = {354--368},
 doi          = {10.1007/978-3-540-87531-4_26},
)
@inproceedings(emerson1991tree,
 author       = {E Allen Emerson and Charanjit S Jutla},
 year         = {1991},
 title        = {Tree automata, mu-calculus and determinacy},
 booktitle    = {Foundations of Computer Science, 1991. Proceedings., 32nd Annual Symposium on},
 organization = {IEEE},
 pages        = {368--377},
 doi          = {10.1109/SFCS.1991.185392},
)
@article(janin1995automata,
 author       = {David Janin and Igor Walukiewicz},
 year         = {1995},
 title        = {Automata for the modal $\mu$-calculus and related results},
 doi          = {10.1007/3-540-60246-1_160},
)
@article(Kozen1983333,
 author       = {Dexter Kozen},
 year         = {1983},
 title        = {Results on the propositional $\mu$-calculus},
 journal      = {Theoretical Computer Science},
 volume       = {27},
 number       = {3},
 pages        = {333--354},
 doi          = {10.1016/0304-3975(82)90125-6},
 note         = {Special Issue Ninth International Colloquium on Automata, Languages and Programming (ICALP) Aarhus, Summer 1982},
)
@article(kozen1988finite,
 author       = {Dexter Kozen},
 year         = {1988},
 title        = {A finite model theorem for the propositional $\mu$-calculus},
 journal      = {Studia Logica},
 volume       = {47},
 number       = {3},
 pages        = {233--241},
 doi          = {10.1007/BF00370554},
)
@article(kupferman2000automata,
 author       = {Orna Kupferman and Moshe Y Vardi and Pierre Wolper},
 year         = {2000},
 title        = {An automata-theoretic approach to branching-time model checking},
 journal      = {Journal of the ACM (JACM)},
 volume       = {47},
 number       = {2},
 pages        = {312--360},
 doi          = {10.1145/333979.333987},
)
@article(kusters2002deciding,
 author       = {Ralf K\"{u}sters and Thomas Wilke},
 year         = {2002},
 title        = {{Deciding the First Level of the $\mu$-calculus Alternation Hierarchy}},
 number       = {0209},
 doi          = {10.1007/3-540-36206-1_22},
)
@article(lehtinendisjunctive,
 author       = {Karoliina Lehtinen},
 year         = {2015},
 title        = {Disjunctive form and the modal $\mu$ alternation hierarchy},
 journal      = {FICS15, The 10th International Workshop on Fixed Points in Computer Science, EPTCS 191},
 pages        = {117},
 doi          = {10.4204/EPTCS.191.11},
)
@inproceedings(lehtinen2015deciding,
 author       = {Karoliina Lehtinen and Sandra Quickert},
 year         = {2015},
 title        = {Deciding the first levels of the modal $\mu$ alternation hierarchy by formula construction},
 booktitle    = {LIPIcs-Leibniz International Proceedings in Informatics},
 volume       = {41},
 organization = {Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik},
 doi          = {10.4230/LIPIcs.CSL.2015.457},
)
@inproceedings(lehtinen2017accepted,
 author       = {Karoliina Lehtinen and Sandra Quickert},
 year         = {2017},
 title        = {{$\Sigma^{\mu}_2$ is decidable for $\Pi^{\mu}_2$}},
 booktitle    = {Unveiling Dynamics and Complexity - 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, Proceedings},
 pages        = {292--303},
 doi          = {10.1007/978-3-319-58741-7_28},
)
@incollection(lenzi-strict,
 author       = {Giacomo Lenzi},
 year         = {1996},
 title        = {A hierarchy theorem for the $\mu$-calculus},
 editor       = {Friedhelm Meyer and Burkhard Monien},
 booktitle    = {Automata, Languages and Programming},
 series       = {Lecture Notes in Computer Science},
 volume       = {1099},
 publisher    = {Springer Berlin Heidelberg},
 pages        = {87--97},
 doi          = {10.1007/3-540-61440-0_119},
)
@article(martin1975borel,
 author       = {Donald A Martin},
 year         = {1975},
 title        = {Borel determinacy},
 journal      = {Annals of Mathematics},
 pages        = {363--371},
 doi          = {10.2307/1971035},
)
@incollection(MateescuRadu2002,
 author       = {Radu Mateescu},
 year         = {2002},
 title        = {Local Model-Checking of Modal Mu-Calculus on Acyclic Labeled Transition Systems},
 editor       = {Joost-Pieter Katoen and Perdita Stevens},
 booktitle    = {Tools and Algorithms for the Construction and Analysis of Systems},
 series       = {Lecture Notes in Computer Science},
 volume       = {2280},
 publisher    = {Springer Berlin Heidelberg},
 pages        = {281--295},
 doi          = {10.1007/3-540-46002-0_20},
)
@inbook(niwinski1986fixed,
 author       = {Damian Niwi\'{n}ski},
 year         = {1986},
 title        = {On fixed-point clones},
 pages        = {464--473},
 publisher    = {Springer Berlin Heidelberg},
 address      = {Berlin, Heidelberg},
 doi          = {10.1007/3-540-16761-7_96},
)
@inbook(otto1999eliminating,
 author       = {Martin Otto},
 year         = {1999},
 title        = {Eliminating Recursion in the $\mu$-Calculus},
 pages        = {531--540},
 publisher    = {Springer Berlin Heidelberg},
 address      = {Berlin, Heidelberg},
 doi          = {10.1007/3-540-49116-3_50},
)
@inproceedings(skrzypczakdeciding,
 author       = {Michal Skrzypczak and Igor Walukiewicz},
 year         = {2016},
 title        = {{Deciding the Topological Complexity of B\"{u}chi Languages}},
 editor       = {Yuval Rabani {Ioannis Chatzigiannakis}, Michael Mitzenmacher and Davide Sangiorgi},
 booktitle    = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
 series       = {Leibniz International Proceedings in Informatics (LIPIcs)},
 volume       = {55},
 publisher    = {Schloss Dagstuhl--Leibniz-Zentrum f\"{u}r Informatik},
 address      = {Dagstuhl, Germany},
 pages        = {99:1--99:13},
 doi          = {10.4230/LIPIcs.ICALP.2016.99},
)
@article(walukiewicz2002monadic,
 author       = {Igor Walukiewicz},
 year         = {2002},
 title        = {Monadic second-order logic on tree-like structures},
 journal      = {Theoretical Computer Science},
 volume       = {275},
 number       = {1},
 pages        = {311--346},
 doi          = {10.1016/S0304-3975(01)00185-2},
)