A. Bianco, F. Mogavero, and A. Murano, Graded computation tree logic, LICS, 2009.
DOI : 10.1145/2287718.2287725
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.8955

P. Bonatti, C. Lutz, A. Murano, and M. Vardi, The complexity of enriched µ-calculi, ICALP, 2006.

J. Clark and S. Derose, XML path language (XPath) version 1.0, 1999.

D. Colazzo, G. Ghelli, and C. Sartiani, Efficient asymmetric inclusion between regular expression types, Proceedings of the 12th International Conference on Database Theory, ICDT '09, 2009.
DOI : 10.1145/1514894.1514916
URL : https://hal.archives-ouvertes.fr/inria-00536884

S. Dal-zilio, D. Lugiez, and C. Meyssonnier, A logic you can count on, POPL, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00071562

S. Demri and D. Lugiez, Presburger Modal Logic Is PSPACE-Complete, IJCAR, 2006.
DOI : 10.1007/11814771_44

W. Gelade, Succinctness of regular expressions with interleaving, intersection and counting, MFCS, 2008.

W. Gelade, M. Gyssens, and W. Martens, Regular expressions with counting: Weak versus strong determinism, MFCS, 2009.

W. Gelade, W. Martens, and F. Neven, Optimizing Schema Languages for XML: Numerical Constraints and Interleaving, SIAM Journal on Computing, vol.38, issue.5, 2008.
DOI : 10.1137/070697367

P. Genevès, N. Laya¨?dalaya¨?da, and A. Schmitt, Efficient static analysis of XML paths and types, PLDI, 2007.

P. Genevès and K. Rose, Compiling XPath for streaming access policy, Proceedings of the 2005 ACM symposium on Document engineering , DocEng '05, 2005.
DOI : 10.1145/1096601.1096617

P. Habermehl, R. Iosif, and T. Vojnar, Automata-based verification of programs with tree updates, Acta Informatica, vol.24, issue.3, pp.1-31, 2010.
DOI : 10.1007/s00236-009-0108-5
URL : https://hal.archives-ouvertes.fr/hal-00150145

J. G. Henriksen, J. Jensen, M. Jørgensen, N. Klarlund, B. Paige et al., Mona: Monadic second-order logic in practice, TACAS, 1995.

H. Hosoya, J. Vouillon, and B. C. Pierce, Regular expression types for XML, ACM Transactions on Programming Languages and Systems, vol.27, issue.1, pp.46-90, 2005.
DOI : 10.1145/1053468.1053470
URL : https://hal.archives-ouvertes.fr/hal-00009271

P. Kilpelinen and R. Tuhkanen, One-unambiguity of regular expressions with numeric occurrence indicators, Information and Computation, vol.205, issue.6, pp.890-916, 2007.
DOI : 10.1016/j.ic.2006.12.003

F. Klaedtke and H. Rueß, Monadic Second-Order Logics with Cardinalities, ICALP, 2003.
DOI : 10.1007/3-540-45061-0_54

N. Klarlund and A. Møller, MONA Version 1.4 User Manual. BRICS Notes Series NS-01-1, 2001.

D. Kozen, Results on the Propositional ??-Calculus, ICALP, 1982.
DOI : 10.7146/dpb.v11i146.7420

O. Kupferman, U. Sattler, and M. Y. Vardi, The complexity of the graded µ-calculus, CADE, 2002.

Z. Manna, H. B. Sipma, and T. Zhang, Verifying Balanced Trees, LFCS, 2007.
DOI : 10.1007/978-3-540-72734-7_26
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.1385

R. Albert, L. J. Meyer, and . Stockmeyer, The equivalence problem for regular expressions with squaring requires exponential space, FOCS, 1972.

M. Murata, D. Lee, M. Mani, and K. Kawaguchi, Taxonomy of XML schema languages using formal language theory, ACM Transactions on Internet Technology, vol.5, issue.4, pp.660-704, 2005.
DOI : 10.1145/1111627.1111631

U. Sattler and M. Y. Vardi, The hybrid µ-calculus, IJCAR, 2001.

H. Seidl, T. Schwentick, A. Muscholl, and P. Habermehl, Counting in Trees for Free, ICALP, 2004.
DOI : 10.1007/978-3-540-27836-8_94
URL : https://hal.archives-ouvertes.fr/hal-00159525

A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics, vol.5, issue.2, pp.285-309, 1955.
DOI : 10.2140/pjm.1955.5.285

C. Balder-ten and M. Marx, Axiomatizing the logical core of XPath 2.0. Theor, Comp. Sys, vol.44, issue.4, pp.561-589, 2009.

W. James, J. B. Thatcher, and . Wright, Generalized finite automata theory with an application to a decision problem of second-order logic, Mathematical Systems Theory, vol.2, issue.1, pp.57-81, 1968.

M. Y. Vardi, Reasoning about the past with two-way automata, ICALP, 1998.
DOI : 10.1007/BFb0055090

K. Zee, V. Kuncak, and M. Rinard, Full functional verification of linked data structures, PLDI, 2008.