L. Automata and I. Games, A Guide to Current Research [outcome of a Dagstuhl seminar, Lecture Notes in Computer Science, vol.2500, 2001.

]. T. Apo76, Introduction to Analytic Number Theory, 1976.

[. Berwanger and A. Blumensath, The Monadic Theory of Tree-like Structures, Automata, Logics, and Infinite Games [ALI02], pp.285-302
DOI : 10.1007/3-540-36387-4_16

M. Brambilla, S. Ceri, S. Comai, P. Fraternali, and I. Manolescu, Specification and Design of Workflow-Driven Hypertexts, J. Web Eng, vol.1, issue.2, pp.163-182, 2003.

C. Bojanczyk and . David, Anca Muscholl, Thomas Schwentick, and Luc Segoufin. Two-variable logic on data words, ACM Trans. Comput. Log, vol.12, issue.4, p.27, 2011.

A. Bès, An application of the Feferman-Vaught theorem to automata and logics for words over an infinite alphabet, Logical Methods in Computer Science, vol.4, issue.18, pp.1-23, 2008.

A. Blumensath and E. Grädel, Automatic structures, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332), pp.51-62
DOI : 10.1109/LICS.2000.855755

A. Bouajjani, P. Habermehl, Y. Jurski, and M. Sighireanu, Rewriting Systems with Data, FCT [FCT07], pp.1-22
DOI : 10.1007/978-3-540-74240-1_1
URL : https://hal.archives-ouvertes.fr/hal-00157782

A. Bouajjani, P. Habermehl, and R. Mayr, Automatic verification of recursive procedures with one integer parameter, Theoretical Computer Science, vol.295, issue.1-3, pp.85-106, 2003.
DOI : 10.1016/S0304-3975(02)00397-3
URL : https://hal.archives-ouvertes.fr/hal-00148237

[. Benedikt, L. Libkin, T. Schwentick, and L. Segoufin, Definable relations and first-order query languages over strings, Journal of the ACM, vol.50, issue.5, pp.694-751, 2003.
DOI : 10.1145/876638.876642

S. Robert, J. Boyer, and . Strother-moore, A fast string searching algorithm, Commun . ACM, vol.20, issue.10, pp.762-772, 1977.

R. Aaron, Z. Bradley, and . Manna, The Calculus of Computation : Decision Procedures with Applications to Verification, 2007.

A. Bojanczyk, T. Muscholl, L. Schwentick, C. Segoufin, and . David, Two-Variable Logic on Words with Data, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), pp.7-16
DOI : 10.1109/LICS.2006.51
URL : https://hal.archives-ouvertes.fr/hal-00151749

M. Bojanczyk, A. Muscholl, T. Schwentick, and L. Segoufin, Two-variable logic on data trees and XML reasoning, J. ACM Brzozowski. Derivatives of Regular Expressions. J. ACM, vol.56, issue.114, pp.481-494, 1964.
URL : https://hal.archives-ouvertes.fr/hal-00151833

]. J. Büc60 and . Büchi, Weak second-order arithmetic and finite automata, Z. Math. Logik und grundl. Math, vol.6, pp.66-92, 1960.

C. Choffrut and S. Grigorieff, The ???equal last letter??? predicate for words on infinite alphabets and classes of multitape automata, Theoretical Computer Science, vol.410, issue.30-32, pp.30-322870, 2009.
DOI : 10.1016/j.tcs.2009.01.034

C. Choffrut and S. Grigorieff, Finite n-tape automata over possibly infinite alphabets: Extending a theorem of Eilenberg et al., Theoretical Computer Science, vol.410, issue.1, pp.16-34, 2009.
DOI : 10.1016/j.tcs.2008.07.018

[. Cole, L. Gottlieb, and M. Lewenstein, Dictionary matching and indexing with errors and don't cares, Proceedings of the thirty-sixth annual ACM symposium on Theory of computing , STOC '04, pp.91-100
DOI : 10.1145/1007352.1007374

T. W. Ho-leung-chan, . Lam, . Wing-kin, S. Sung, S. Tam et al., Compressed Indexes for??Approximate String Matching, Algorithmica, vol.17, issue.2, pp.263-281, 2010.
DOI : 10.1007/s00453-008-9263-2

R. Cox, Minimal number of edges in ?-free non-deterministic finite automata (NFA) for regular expression (1 + ?) · (2 + ?) · (3 + ?) · · · (n + ?). The On-Line Encyclopedia of Integer Sequences, Sequence A129403oeis.org/A129403. [COZ09], 2007.

J. Champarnaud, F. Ouardi, and D. Ziadi, An efficient computation of the equation K-automaton of a regular K-expression, Fundamenta Mathematica, vol.90, issue.12, pp.1-16, 2009.

S. Demri, R. Lazi´clazi´c, and D. Nowak, On the freeze quantifier in Constraint LTL: Decidability and complexity, Information and Computation, vol.205, issue.1, pp.2-24, 2007.
DOI : 10.1016/j.ic.2006.08.003

S. Demri, R. Lazic, and A. Sangnier, Model Checking Freeze LTL over One-Counter Automata, FoSSaCS [FoS08], pp.490-504
DOI : 10.1007/978-3-540-78499-9_34

[. Eilenberg, C. Elgot, and J. Shepherdson, Sets recognized by n-tape automata, Journal of Algebra, vol.13, issue.4, pp.447-464, 1969.
DOI : 10.1016/0021-8693(69)90107-0

A. Ehrenfeucht, An Application of Games to the Completeness Problem for Formalized Theories, Fundamenta Mathematicae, vol.49, pp.129-141, 1961.

]. S. Eil74 and . Eilenberg, Automata, languages, and machines. Pure and Applied Mathematics, 1974.

B. Herbert and . Enderton, A Mathematical Introduction to Logic, 1972.

M. Farach, Optimal suffix tree construction with large alphabets, Proceedings 38th Annual Symposium on Foundations of Computer Science, p.137, 1997.
DOI : 10.1109/SFCS.1997.646102

J. Ferrante and C. Rackoff, A Decision Procedure for the First Order Theory of Real Addition with Order, SIAM Journal on Computing, vol.4, issue.1, pp.69-76, 1975.
DOI : 10.1137/0204006

]. R. Fra54 and . Fraïssé, Sur Quelques Classifications des Systèmes de Relations, Publ. Sci. Univ. Alger. Sér. A, vol.1, pp.35-182, 1954.

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009.
DOI : 10.1017/CBO9780511801655
URL : https://hal.archives-ouvertes.fr/inria-00072739

R. [. Feferman and . Vaught, The first order properties of products of algebraic systems, Fundamenta Mathematicae, vol.47, issue.1, pp.57-103, 1959.

V. Geffert, Translation of binary regular expressions into nondeterministic ??-free automata with O(nlogn) transitions, LATA [LAT10], pp.451-472, 2003.
DOI : 10.1016/S0022-0000(03)00036-9

[. Glushkov, THE ABSTRACT THEORY OF AUTOMATA, Russian Mathematical Surveys, vol.16, issue.5, pp.1-53, 1961.
DOI : 10.1070/RM1961v016n05ABEH004112

C. Hagenah and A. Muscholl, Computing ?-free NFA from Regular Expressions in O(n log 2 (n)) Time. RAIRO -Theoretical Informatics and Applications, pp.257-277, 2000.

J. E. Hopcroft, R. Motwani, and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, 2006.

]. B. Hod83 and . Hodgson, Décidabilité par automate fini, Ann. Sci. Math. Quebec, vol.7, pp.39-57, 1983.

J. Hopcroft, AN n log n ALGORITHM FOR MINIMIZING STATES IN A FINITE AUTOMATON, Theory of Machines and Computations, pp.189-196, 1971.
DOI : 10.1016/B978-0-12-417750-5.50022-1

[. Hromkovi?, S. Seibert, and T. Wilke, Translating Regular Expressions into Small ??-Free Nondeterministic Finite Automata, Journal of Computer and System Sciences, vol.62, issue.4, pp.565-588, 2001.
DOI : 10.1006/jcss.2001.1748

M. Kaminski and N. Francez, Finite-memory automata, Theoretical Computer Science, vol.134, issue.2, pp.329-363, 1994.
DOI : 10.1016/0304-3975(94)90242-9

D. Kuske and M. Lohrey, Decidable Theories of Cayley-Graphs, STACS [STA03], pp.463-474
DOI : 10.1007/3-540-36494-3_41

D. Kuske and M. Lohrey, Monadic Chain Logic Over Iterations and Applications to Pushdown Systems, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), pp.91-100
DOI : 10.1109/LICS.2006.35

]. S. Kle56 and . Kleene, Representation of events in nerve nets and finite automata, Automata Studies, pp.3-41, 1956.

[. Karch, D. Luxen, and P. Sanders, Improved Fast Similarity Search in Dictionaries, Chávez and Lonardi [CL10], pp.173-178
DOI : 10.1007/978-3-642-16321-0_16

[. Khoussainov and A. Nerode, Automatic presentations of structures, LCC [LCC95], pp.367-392
DOI : 10.1007/3-540-60178-3_93

M. Richard, M. O. Karp, and . Rabin, Efficient randomized pattern-matching algorithms, IBM J. Res. Dev, vol.31, issue.2, pp.249-260, 1987.

Y. Lifshits, A lower bound on the size of ??-free NFA corresponding to a regular expression, Information Processing Letters, vol.85, issue.6, pp.293-299, 2003.
DOI : 10.1016/S0020-0190(02)00436-2

[. Lombardy and J. Sakarovitch, The universal automaton, Logic and Automata, pp.457-504, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00620807

[. Loos and V. Weispfenning, Applying Linear Quantifier Elimination, The Computer Journal, vol.36, issue.5, pp.450-462, 1993.
DOI : 10.1093/comjnl/36.5.450

M. Edward and . Mccreight, A Space-Economical Suffix Tree Construction Algorithm, J. ACM, vol.23, issue.2, pp.262-272, 1976.

F. Edward and . Moore, Gedanken-experiments on sequential machines, Automata studies, pp.129-153, 1956.

A. Mostowski, On direct products of theories, The Journal of Symbolic Logic, vol.I, issue.01, pp.1-31, 1952.
DOI : 10.2307/2267454

]. J. Myh57 and . Myhill, Finite automata and the representation of events, Ohio, 1957.

]. A. Ner58 and . Nerode, Linear automata transformation, Proceedings of the American Mathematical Society, pp.541-544, 1958.

[. Neven, T. Schwentick, and V. Vianu, Towards Regular Languages over Infinite Alphabets, MFCS [MFC01], pp.560-572
DOI : 10.1007/3-540-44683-4_49

D. Ouardi and . Ziadi, Efficient weighted expressions conversion, Theoretical Informatics and Applications, pp.285-307, 2008.
DOI : 10.1051/ita:2007035
URL : https://hal.archives-ouvertes.fr/hal-00466632

[. Presburger and D. Jabcquette, On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation, History and Philosophy of Logic, vol.12, issue.2, pp.225-233, 1991.
DOI : 10.1080/014453409108837187

M. Presburger, Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt . Spra-wozdanie z I Kongresu matematyków krajów sl owiá n skich Decidability of second-order theories and automata on infinite trees, pp.92-1011, 1929.

M. O. Rabin, Decidable Theories, Handbook of Mathematical Logic, pp.595-629, 1977.
DOI : 10.1016/S0049-237X(08)71116-9

D. Revuz, Minimisation of acyclic deterministic automata in linear time, Theoretical Computer Science, vol.92, issue.1, pp.181-189, 1992.
DOI : 10.1016/0304-3975(92)90142-3
URL : https://hal.archives-ouvertes.fr/hal-00619678

]. R. Rob58 and . Robinson, Restricted set-theoretical definitions in arithmetic, Proc. Am, pp.238-242, 1958.

D. [. Rabin and . Scott, Finite Automata and Their Decision Problems, IBM Journal of Research and Development, vol.3, issue.2, pp.114-125, 1959.
DOI : 10.1147/rd.32.0114

S. Rubin, Abstract, Bulletin of Symbolic Logic, vol.2285, issue.02, pp.169-209, 2008.
DOI : 10.1007/s00224-004-1133-y

J. Sakarovitch, éléments de théorie des automates. Les Classiques de l'informatique, 2003.

G. Schnitger, Regular expressions and nfas without epsilon-transitions, STACS [sta06], pp.432-443

A. L. Semenov, Decidability of monadic theories, MFCS [MFC84], pp.162-175
DOI : 10.1007/BFb0030296

Y. Shemesh and N. Francez, Finite-State Unification Automata and Relational Languages, Information and Computation, vol.114, issue.2, pp.192-213, 1994.
DOI : 10.1006/inco.1994.1085

S. Shelah, The Monadic Theory of Order, The Annals of Mathematics, vol.102, issue.3, pp.379-419, 1975.
DOI : 10.2307/1971037

J. Stupp, The lattice-model is recursive in the original model, 1975.

[. Tan, On pebble automata for data languages with decidable emptiness problem, Journal of Computer and System Sciences, vol.76, issue.8, pp.778-791, 2010.
DOI : 10.1016/j.jcss.2010.03.004

W. Thomas-automata and L. , Handbook of formal languages, pp.389-455, 1997.

T. Tsankov, Abstract, The Journal of Symbolic Logic, vol.35, issue.04, pp.1341-1351, 2011.
DOI : 10.2178/jsl/1318338853

E. Ukkonen, Constructing suffix trees on-line in linear time, Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture -Information Processing '92, pp.484-492, 1992.

E. Ukkonen, On-line construction of suffix trees, Algorithmica, vol.10, issue.3, pp.249-260, 1995.
DOI : 10.1007/BF01206331

[. Vianu, Automatic verification of database-driven systems, Proceedings of the 12th International Conference on Database Theory, ICDT '09, pp.1-13
DOI : 10.1145/1514894.1514896

R. Villemaire, Joining k- and l-recognizable sets of natural numbers, STACS [STA92], pp.83-94
DOI : 10.1007/3-540-55210-3_175

I. Walukiewicz, Monadic second-order logic on tree-like structures, Theoretical Computer Science, vol.275, issue.1-2, pp.311-346, 2002.
DOI : 10.1016/S0304-3975(01)00185-2

P. Weiner, Linear pattern matching algorithms, 14th Annual Symposium on Switching and Automata Theory (swat 1973), pp.1-11, 1973.
DOI : 10.1109/SWAT.1973.13

S. Yu, Handbook of Formal Languages, chapter Regular Languages, pp.41-110, 1998.