@article(achim-pumping,
 author       = {Achim Blumensath},
 year         = {2008},
 title        = {On the Structure of Graphs in the {C}aucal Hierarchy},
 journal      = {Theor. Comput. Sci.},
 volume       = {400},
 number       = {1-3},
 pages        = {19--45},
 doi          = {10.1016/j.tcs.2008.01.053},
)
@article(achim-erratum,
 author       = {Achim Blumensath},
 year         = {2013},
 title        = {Erratum to "On the Structure of Graphs in the {C}aucal Hierarchy" [Theoret. Comput. Sci 400 {(2008)} 19-45]},
 journal      = {Theor. Comput. Sci.},
 volume       = {475},
 pages        = {126--127},
 doi          = {10.1016/j.tcs.2012.12.044},
)
@inproceedings(DBLP:conf/stacs/BojanczykT12,
 author       = {Miko{\l}aj Boja{\'{n}}czyk and Szymon Toru{\'{n}}czyk},
 year         = {2012},
 title        = {Weak {MSO+U} over Infinite Trees},
 editor       = {Christoph D{\"{u}}rr and Thomas Wilke},
 booktitle    = {29th International Symposium on Theoretical Aspects of Computer Science, {STACS} 2012, February 29th - March 3rd, 2012, Paris, France},
 series       = {LIPIcs},
 volume       = {14},
 publisher    = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
 pages        = {648--660},
 doi          = {10.4230/LIPIcs.STACS.2012.648},
)
@inproceedings(saturation,
 author       = {Christopher H. Broadbent and Arnaud Carayol and Matthew Hague and Olivier Serre},
 year         = {2012},
 title        = {A Saturation Method for Collapsible Pushdown Systems},
 editor       = {Artur Czumaj and Kurt Mehlhorn and Andrew M. Pitts and Roger Wattenhofer},
 booktitle    = {Automata, Languages, and Programming - 39th International Colloquium, {ICALP} 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part {II}},
 series       = {Lecture Notes in Computer Science},
 volume       = {7392},
 publisher    = {Springer},
 pages        = {165--176},
 doi          = {10.1007/978-3-642-31585-5\_18},
)
@inproceedings(DBLP:conf/csl/BroadbentK13,
 author       = {Christopher H. Broadbent and Naoki Kobayashi},
 year         = {2013},
 title        = {Saturation-Based Model Checking of Higher-Order Recursion Schemes},
 editor       = {Simona Ronchi Della Rocca},
 booktitle    = {Computer Science Logic 2013 {(CSL} 2013), {CSL} 2013, September 2-5, 2013, Torino, Italy},
 series       = {LIPIcs},
 volume       = {23},
 publisher    = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
 pages        = {129--148},
 doi          = {10.4230/LIPIcs.CSL.2013.129},
)
@inproceedings(downward-closure,
 author       = {Lorenzo Clemente and Pawel Parys and Sylvain Salvati and Igor Walukiewicz},
 year         = {2016},
 title        = {The Diagonal Problem for Higher-Order Recursion Schemes is Decidable},
 editor       = {Martin Grohe and Eric Koskinen and Natarajan Shankar},
 booktitle    = {Proceedings of the 31st Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} '16, New York, NY, USA, July 5-8, 2016},
 publisher    = {{ACM}},
 pages        = {96--105},
 doi          = {10.1145/2933575.2934527},
)
@inproceedings(DBLP:conf/fsttcs/ClementePSW15,
 author       = {Lorenzo Clemente and Pawe\IeC{\l} Parys and Sylvain Salvati and Igor Walukiewicz},
 year         = {2015},
 title        = {Ordered Tree-Pushdown Systems},
 editor       = {Prahladh Harsha and G. Ramalingam},
 booktitle    = {35th {IARCS} Annual Conference on Foundation of Software Technology and Theoretical Computer Science, {FSTTCS} 2015, December 16-18, 2015, Bangalore, India},
 series       = {LIPIcs},
 volume       = {45},
 publisher    = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
 pages        = {163--177},
 doi          = {10.4230/LIPIcs.FSTTCS.2015.163},
)
@article(Damm82,
 author       = {Werner Damm},
 year         = {1982},
 title        = {The {IO-} and OI-Hierarchies},
 journal      = {Theor. Comput. Sci.},
 volume       = {20},
 pages        = {95--207},
 doi          = {10.1016/0304-3975(82)90009-3},
)
@inproceedings(diagonal-safe,
 author       = {Matthew Hague and Jonathan Kochems and C.{-}H. Luke Ong},
 year         = {2016},
 title        = {Unboundedness and Downward Closures of Higher-Order Pushdown Automata},
 editor       = {Bod{\'{\i}}k, Rastislav and Rupak Majumdar},
 booktitle    = {Proceedings of the 43rd Annual {ACM} {SIGPLAN-SIGACT} Symposium on Principles of Programming Languages, {POPL} 2016, St. Petersburg, FL, USA, January 20 - 22, 2016},
 publisher    = {{ACM}},
 pages        = {151--163},
 doi          = {10.1145/2837614.2837627},
)
@inproceedings(collapsible,
 author       = {Matthew Hague and Andrzej S. Murawski and C.{-}H. Luke Ong and Olivier Serre},
 year         = {2008},
 title        = {Collapsible Pushdown Automata and Recursion Schemes},
 booktitle    = {Proceedings of the Twenty-Third Annual {IEEE} Symposium on Logic in Computer Science, {LICS} 2008, 24-27 June 2008, Pittsburgh, PA, {USA}},
 publisher    = {{IEEE} Computer Society},
 pages        = {452--461},
 doi          = {10.1109/LICS.2008.34},
)
@inproceedings(Kar-Par-pumping,
 author       = {Alexander Kartzow and Pawe\IeC{\l} Parys},
 year         = {2012},
 title        = {Strictness of the Collapsible Pushdown Hierarchy},
 editor       = {Branislav Rovan and Vladimiro Sassone and Peter Widmayer},
 booktitle    = {Mathematical Foundations of Computer Science 2012 - 37th International Symposium, {MFCS} 2012, Bratislava, Slovakia, August 27-31, 2012. Proceedings},
 series       = {Lecture Notes in Computer Science},
 volume       = {7464},
 publisher    = {Springer},
 pages        = {566--577},
 doi          = {10.1007/978-3-642-32589-2\_50},
)
@inproceedings(KNU-hopda,
 author       = {Teodor Knapik and Niwi\IeC{\'n}ski, Damian and Pawe\IeC{\l} Urzyczyn},
 year         = {2002},
 title        = {Higher-Order Pushdown Trees Are Easy},
 editor       = {Mogens Nielsen and Uffe Engberg},
 booktitle    = {Foundations of Software Science and Computation Structures, 5th International Conference, {FOSSACS} 2002. Held as Part of the Joint European Conferences on Theory and Practice of Software, {ETAPS} 2002 Grenoble, France, April 8-12, 2002, Proceedings},
 series       = {Lecture Notes in Computer Science},
 volume       = {2303},
 publisher    = {Springer},
 pages        = {205--222},
 doi          = {10.1007/3-540-45931-6\_15},
)
@inproceedings(kobayashi2009types-popl,
 author       = {Naoki Kobayashi},
 year         = {2009},
 title        = {Types and Higher-Order Recursion Schemes for Verification of Higher-Order Programs},
 editor       = {Zhong Shao and Benjamin C. Pierce},
 booktitle    = {Proceedings of the 36th {ACM} {SIGPLAN-SIGACT} Symposium on Principles of Programming Languages, {POPL} 2009, Savannah, GA, USA, January 21-23, 2009},
 publisher    = {{ACM}},
 pages        = {416--428},
 doi          = {10.1145/1480881.1480933},
)
@inproceedings(koba-pumping,
 author       = {Naoki Kobayashi},
 year         = {2013},
 title        = {Pumping by Typing},
 booktitle    = {28th Annual {ACM/IEEE} Symposium on Logic in Computer Science, {LICS} 2013, New Orleans, LA, USA, June 25-28, 2013},
 publisher    = {{IEEE} Computer Society},
 pages        = {398--407},
 doi          = {10.1109/LICS.2013.46},
)
@inproceedings(context-sensitive-2,
 author       = {Naoki Kobayashi and Kazuhiro Inaba and Takeshi Tsukada},
 year         = {2014},
 title        = {Unsafe Order-2 Tree Languages Are Context-Sensitive},
 editor       = {Anca Muscholl},
 booktitle    = {Foundations of Software Science and Computation Structures - 17th International Conference, {FOSSACS} 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, {ETAPS} 2014, Grenoble, France, April 5-13, 2014, Proceedings},
 series       = {Lecture Notes in Computer Science},
 volume       = {8412},
 publisher    = {Springer},
 pages        = {149--163},
 doi          = {10.1007/978-3-642-54830-7\_10},
)
@inproceedings(kobayashiOng2009type,
 author       = {Naoki Kobayashi and C.{-}H. Luke Ong},
 year         = {2009},
 title        = {A Type System Equivalent to the Modal Mu-Calculus Model Checking of Higher-Order Recursion Schemes},
 booktitle    = {Proceedings of the 24th Annual {IEEE} Symposium on Logic in Computer Science, {LICS} 2009, 11-14 August 2009, Los Angeles, CA, {USA}},
 publisher    = {{IEEE} Computer Society},
 pages        = {179--188},
 doi          = {10.1109/LICS.2009.29},
)
@inproceedings(Ong-hoschemes,
 author       = {C.{-}H. Luke Ong},
 year         = {2006},
 title        = {On Model-Checking Trees Generated by Higher-Order Recursion Schemes},
 booktitle    = {21th {IEEE} Symposium on Logic in Computer Science {(LICS} 2006), 12-15 August 2006, Seattle, WA, USA, Proceedings},
 publisher    = {{IEEE} Computer Society},
 pages        = {81--90},
 doi          = {10.1109/LICS.2006.38},
)
@article(jfp-numerals,
 author       = {Pawel Parys},
 year         = {2016},
 title        = {A Characterization of Lambda-Terms Transforming Numerals},
 journal      = {J. Funct. Program.},
 volume       = {26},
 pages        = {e12},
 doi          = {10.1017/S0956796816000113},
)
@inproceedings(ho-new,
 author       = {Pawe\IeC{\l} Parys},
 year         = {2012},
 title        = {On the Significance of the Collapse Operation},
 booktitle    = {Proceedings of the 27th Annual {IEEE} Symposium on Logic in Computer Science, {LICS} 2012, Dubrovnik, Croatia, June 25-28, 2012},
 publisher    = {{IEEE} Computer Society},
 pages        = {521--530},
 doi          = {10.1109/LICS.2012.62},
)
@article(itrs-arxiv,
 author       = {Pawe\IeC{\l} Parys},
 year         = {2017},
 title        = {Intersection Types and Counting},
 journal      = {CoRR},
 volume       = {abs/1701.05303v1},
 url          = {http://arxiv.org/abs/1701.05303v1},
)
@inproceedings(DBLP:conf/popl/RamsayNO14,
 author       = {Steven J. Ramsay and Robin P. Neatherway and C.{-}H. Luke Ong},
 year         = {2014},
 title        = {A Type-Directed Abstraction Refinement Approach to Higher-Order Model Checking},
 editor       = {Suresh Jagannathan and Peter Sewell},
 booktitle    = {The 41st Annual {ACM} {SIGPLAN-SIGACT} Symposium on Principles of Programming Languages, {POPL} '14, San Diego, CA, USA, January 20-21, 2014},
 publisher    = {{ACM}},
 pages        = {61--72},
 doi          = {10.1145/2535838.2535873},
)
@article(MSC:9613738,
 author       = {Sylvain Salvati and Igor Walukiewicz},
 year         = {2016},
 title        = {Simply Typed Fixpoint Calculus and Collapsible Pushdown Automata},
 journal      = {Mathematical Structures in Computer Science},
 volume       = {26},
 number       = {7},
 pages        = {1304--1350},
 doi          = {10.1017/S0960129514000590},
)