R. Alur and P. Cern´ycern´y, Expressiveness of streaming string transducers, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, pp.1-12, 2010.

R. Alur and J. V. Deshmukh, Nondeterministic streaming string transducers, Automata, Languages and Programming-38th International Colloquium, Proceedings, Part II, pp.1-20, 2011.

R. Alur, D. Loris, M. Antoni, and . Raghothaman, Drex: A declarative language for efficiently evaluating regular string transformations, Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp.125-137, 2015.

R. Alur, A. Freilich, and M. Raghothaman, Regular combinators for string transformations, Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, vol.9, pp.1-9, 2014.

A. Arnold, A syntactic congruence for rational omega-language, Theor. Comput. Sci, vol.39, pp.333-335, 1985.

M. , P. Béal, and O. Carton, Computing the prefix of an automaton, ITA, vol.34, issue.6, pp.503-514, 2000.

, Determinization of transducers over finite and infinite words, Theor, Comput. Sci, vol.289, issue.1, pp.225-251, 2002.

, Determinization of transducers over infinite words: The general case, Theory

, Comput. Syst, vol.37, issue.4, pp.483-502, 2004.

M. Béal, O. Carton, C. Prieur, and J. Sakarovitch, Squaring transducers: An efficient procedure for deciding functionality and sequentiality of transducers, LATIN 2000: Theoretical Informatics, 4th Latin American Symposium, pp.397-406, 2000.

L. Mikoo-laj-boja´nczykboja´nczyk, B. Daviaud, V. Guillon, and . Penelle, Which classes of origin graphs are generated by transducers, 44th International Colloquium on Automata, Languages, and Programming, vol.114, pp.1-114, 2017.

C. Mikoo-laj-boja´nczykboja´nczyk, A. David, T. Muscholl, L. Schwentick, and . Segoufin, Two-variable logic on data words, ACM Trans. Comput. Log, vol.12, issue.4, pp.1-27, 2011.

J. Berstel, Transductions and context-free languages, Teubner Studienbücher : Informatik, vol.38, 1979.
URL : https://hal.archives-ouvertes.fr/hal-00619779

F. Baschenis, O. Gauwin, A. Muscholl, and G. Puppis, Minimizing resources of sweeping and streaming string transducers, 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, vol.114, pp.1-114, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01274992

, Untwisting two-way transducers in elementary time, 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, pp.1-12, 2017.

J. R. Büchi and L. H. Landweber, Solving sequential conditions by finite-state strategies, Transactions of the American Mathematical Society, vol.138, pp.295-311, 1969.

A. Boiret, A. Lemay, and J. Niehren, Learning rational functions, Developments in Language Theory-16th International Conference, DLT 2012, pp.273-283, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00692341

A. Boiret, Normal form on linear tree-to-word transducers, Language and Automata Theory and Applications-10th International Conference, pp.439-451, 2016.

B. Mikoo-laj, Effective characterizations of tree logics, Proceedings of the Twenty-Seventh ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2008, pp.53-66, 2008.

, Transducers with origin information, Automata, Languages, and Programming-41st International Colloquium, ICALP, pp.26-37, 2014.

, Recognisable languages over monads, Developments in Language Theory19th International Conference, DLT 2015, pp.1-13, 2015.

P. Bouyer, A logical characterization of data languages, Inf. Process. Lett, vol.84, issue.2, pp.75-85, 2002.

M. Mikoo-laj-boja´nczykboja´nczyk and . Pilipczuk, Definability equals recognizability for graphs of bounded treewidth, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, pp.407-416, 2016.

N. Baudru and P. Reynier, From two-way transducers to regular function expressions, Developments in Language Theory-22nd International Conference, Proceedings, 2018.

J. R. Büchi, Weak second-order arithmetic and finite automata, Mathematical Logic Quarterly-MLQ, vol.6, pp.66-92, 1960.

, On a decision method in restricted second order arithmetic, Proc. International Congress on Logic, Method, and Philosophy of Science, pp.1-12, 1962.

O. Carton, Computer Science-Theory and Applications, 5th International Computer Science Symposium in Russia, Right-sequential functions on infinite words, pp.96-106, 2010.

M. Cadilhac, O. Carton, and C. Paperman, Continuity and rational functions, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, vol.115, pp.1-115, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01587614

O. Carton and L. Dartois, Aperiodic two-way transducers and fo-transductions, 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, pp.160-174, 2015.

S. Cho and D. T. Huynh, Finite-automaton aperiodicity is PSpace-complete, Theor. Comput. Sci, vol.88, issue.1, pp.99-116, 1991.

C. Choffrut, Une caracterisation des fonctions sequentielles et des fonctions sous-sequentielles en tant que relations rationnelles, Theor. Comput. Sci, vol.5, issue.3, pp.325-337, 1977.

, Minimizing subsequential transducers: a survey, Theor. Comput. Sci, vol.292, issue.1, pp.131-143, 2003.

A. Church, Application of recursive arithmetic to the problem of circuit synthesis, Journal of Symbolic Logic, vol.28, issue.4, pp.289-290, 1963.

M. Cadilhac, A. Krebs, M. Ludwig, and C. Paperman, A circuit complexity approach to transductions, Mathematical Foundations of Computer Science 2015-40th International Symposium, MFCS 2015, pp.141-153, 2015.

A. Carayol and C. Löding, Uniformization in automata theory, Logic, Methodology and Philosophy of Science-Proceedings of the 14th International Congress, 2011.

O. Carton and M. Michel, Unambiguous Büchi automata, Theor. Comput. Sci, vol.297, issue.1-3, pp.37-81, 2003.

B. Courcelle, The monadic second-order logic of graphs. i. recognizable sets of finite graphs, Inf. Comput, vol.85, issue.1, pp.12-75, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00353765

, Monadic second-order definable graph transductions: A survey, Theor. Comput. Sci, vol.126, issue.1, pp.53-75, 1994.

, The monadic second-order logic of graphs X: linear orderings, Theor. Comput. Sci, vol.160, issue.1&2, pp.87-143, 1996.

T. Colcombet and D. Petrisan, Automata minimization: a functorial approach, 7th Conference on Algebra and Coalgebra in Computer Science, vol.8, pp.1-8, 2017.

D. Olivier-carton, J. Perrin, and . Pin, Automata and semigroups recognizing infinite words, Logic and Automata: History and Perspectives, pp.133-168, 2008.

L. Chaubard, J. Pin, and H. Straubing, Actions, wreath products of C-varieties and concatenation product, Theor. Comput. Sci, vol.356, issue.1-2, pp.73-89, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00112843

L. Dartois, P. Fournier, I. Jecker, and N. Lhote, On reversible transducers, 44th International Colloquium on Automata, Languages, and Programming, vol.113, pp.1-113, 2017.

L. Dartois, E. Filiot, and N. Lhote, Logics for word transductions with synthesis, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, pp.295-304, 2018.

V. Diekert and P. Gastin, First-order definable languages, Logic and Automata: History and Perspectives, pp.261-306, 2008.

P. Volker-diekert, M. Gastin, and . Kufleitner, A survey on small fragments of first-order logic over finite words, Int. J. Found. Comput. Sci, vol.19, issue.3, pp.513-548, 2008.

V. Dave, P. Gastin, and S. Krishna, Regular transducer expressions for regular transformations over infinite words, Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '18, 2018.

L. Daviaud, P. Jecker, D. Reynier, and . Villevalois, Degree of sequentiality of weighted automata, Foundations of Software Science and Computation Structures-20th International Conference, FOSSACS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, vol.2017
URL : https://hal.archives-ouvertes.fr/hal-01782446

S. Uppsala, , pp.215-230, 2017.

V. Diekert and M. Kufleitner, Fragments of first-order logic over infinite words, 26th International Symposium on Theoretical Aspects of Computer Science, pp.325-336, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00359319

. Vrunda-dave, A. Shankara-narayanan-krishna, and . Trivedi, Fo-definable transformations of infinite strings, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, vol.12, 2016.

L. Daviaud, P. Reynier, and J. Talbot, A generalised twinning property for minimisation of cost register automata, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, pp.857-866, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01201704

. Rodrigo-de-souza, Uniformisation of two-way transducers, Language and Automata Theory and Applications-7th International Conference, pp.547-558, 2013.

H. Ebbinghaus and J. Flum, Finite model theory, Perspectives in Mathematical Logic, 1995.

J. Engelfriet and H. J. Hoogeboom, MSO definable string transductions and two-way finite-state transducers, ACM Trans. Comput. Log, vol.2, issue.2, pp.216-254, 2001.

S. Eilenberg, Automata, languages, and machines. A, Pure and applied mathematics, 1974.

, Automata, languages, and machines, 1976.

C. C. Elgot, Decision problems of finite automata design and related arithmetics, Transactions of the American Mathematical Society, vol.98, issue.1, pp.21-51, 1961.

C. Calvin, J. E. Elgot, and . Mezei, On relations defined by generalized finite automata, IBM Journal of Research and Development, vol.9, issue.1, pp.47-68, 1965.

E. Filiot, O. Gauwin, and N. Lhote, First-order definability of rational transductions: An algebraic approach, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, pp.387-396, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01308509

, Aperiodicity of rational functions is PSpace-complete, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2016, vol.13, p.15, 2016.

E. Filiot, Logic-automata connections for transformations, Logic and Its Applications-6th Indian Conference, ICLA 2015, pp.30-57, 2015.

E. Filiot, C. Jecker, S. Löding, and . Winter, On equivalence and uniformisation problems for finite transducers, 43rd International Colloquium on Automata, Languages, and Programming, vol.125, pp.1-125, 2016.

E. Filiot, A. Shankara-narayanan-krishna, and . Trivedi, First-order definable string transformations, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014, pp.147-159, 2014.

E. Filiot, N. Mazzocchi, and J. Raskin, A pattern logic for automata with outputs, Developments in Language Theory-22nd International Conference, DLT2018, Proceedings, pp.10-14, 2018.

E. Filiot and P. Reynier, Transducers, logic and algebra for functions of finite words, SIGLOG News, vol.3, issue.3, pp.4-19, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01475445

M. Eitan, O. H. Gurari, and . Ibarra, A note on finitely-valued and finitely ambiguous transducers, Mathematical Systems Theory, vol.16, issue.1, pp.61-66, 1983.

F. Gire, Two decidability problems for infinite words, Inf. Process. Lett, vol.22, issue.3, pp.135-140, 1986.

E. Grädel and M. Otto, On logics with two variables, Theor. Comput. Sci, vol.224, issue.1-2, pp.73-113, 1999.

J. E. Hopcroft, An n log n algorithm for minimizing states in a finite automaton, 1971.

R. E. Ladner, Application of model theoretic games to discrete linear orders and finite automata, Information and Control, vol.33, issue.4, pp.281-303, 1977.

G. Laurence, A. Lemay, J. Niehren, S. Staworko, and M. Tommasi, Normalization of sequential top-down tree-to-word transducers, Language and Automata Theory and Applications-5th International Conference, pp.354-365, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00566291

C. Löding and S. Winter, Synthesis of deterministic top-down tree transducers from automatic tree relations, Inf. Comput, vol.253, pp.336-354, 2017.

R. Mcnaughton, Testing and generating infinite sequences by a finite automaton, Information and Control, vol.9, issue.5, pp.521-530, 1966.

E. F. Moore, Annals of mathematics studies, Gedanken-experiments on sequential machines, Automata studies, pp.129-153, 1956.

R. Mcnaughton and S. Papert, Counter-free automata, 1971.

A. Manuel, T. Schwentick, and T. Zeume, A short note on two-variable logic with a linear order successor and a preorder successor, 2013.

A. Manuel and T. Zeume, Two-variable logic on 2-dimensional structures, CSL 2013, pp.484-499, 2013.

A. Nerode, Linear automaton transformations, Journal of Symbolic Logic, vol.28, issue.2, pp.173-174, 1963.
DOI : 10.2307/2033204
URL : https://www.ams.org/proc/1958-009-04/S0002-9939-1958-0135681-9/S0002-9939-1958-0135681-9.pdf

J. Niehren, L. Planque, J. Talbot, and S. Tison, N-ary queries by tree automata, Database Programming Languages, 10th International Symposium, pp.217-231, 2005.
DOI : 10.1007/11601524_14
URL : http://hal.inria.fr/docs/00/53/65/22/PDF/n-ary-query.pdf

D. Perrin, Mathematical Foundations of Computer Science, Recent results on automata and infinite words, pp.134-148, 1984.

-. Jean and . Pin, A variety theorem without complementation., Russian Mathematics (iz. VUZ), pp.80-90, 1995.

, Mathematical foundations of automata theory, 2018.

D. Perrin and J. Pin, Infinite Words, Automata, Semigroups, Logic and Games, vol.141, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00112831

A. Pnueli and R. Rosner, On the synthesis of a reactive module, Conference Record of the Sixteenth Annual ACM Symposium on Principles of Programming Languages, pp.179-190, 1989.

C. Prieur, How to decide continuity of rational functions on infinite words, Theor. Comput. Sci, vol.276, issue.1-2, pp.445-447, 2002.

J. Pin and P. Weil, Automata, Languages and Programming, 22nd International Colloquium, vol.95, pp.348-359, 1995.

O. Michael, D. S. Rabin, and . Scott, Finite automata and their decision problems, IBM Journal of Research and Development, vol.3, issue.2, pp.114-125, 1959.

C. Reutenauer and M. P. Schützenberger, Minimization of rational word functions, SIAM J. Comput, vol.20, issue.4, pp.669-685, 1991.

, Variétés et fonctions rationnelles, vol.145, pp.229-240, 1995.

J. Sakarovitch, Elements of automata theory, 2009.

M. Schützenberger, A remark on finite transducers, Information and Control, vol.4, pp.185-196, 1961.

, On finite monoids having only trivial subgroups, Information and Control, vol.8, issue.2, pp.190-194, 1965.

, Semigroup Forum, vol.13, issue.1, pp.47-75, 1976.

, Sur les relations rationnelles entre monoides libres, Theor. Comput. Sci, vol.3, issue.2, pp.243-259, 1976.

I. Simon, Piecewise testable events, Automata Theory and Formal Languages, 2nd GI Conference, pp.214-222, 1975.

H. Straubing, Finite automata, formal logic, and circuit complexity, Progress in Computer Science and Applied Series, 1994.

T. Schwentick and T. Zeume, Two-variable logic with two order relations, Logical Methods in Computer Science, vol.8, issue.1, 2012.

T. Tan, Extending two-variable logic on data trees with order on data values and its automata, ACM Trans. Comput. Log, vol.15, issue.1, pp.1-8, 2014.

W. Thomas, Star-free regular sets of omega-sequences, Information and Control, vol.42, issue.2, pp.148-156, 1979.

, A combinatorial approach to the theory of omega-automata, Information and Control, vol.48, issue.3, pp.261-283, 1981.

, Facets of synthesis: Revisiting church's problem, Foundations of Software Science and Computational Structures, 12th International Conference, FOSSACS 2009, Held as Part of the Joint European Conferences on Theory and Practice of Software, pp.1-14, 2009.

B. A. Trakhtenbrot, Finite automata and the logic of monadic predicates, Doklady Akademii Nauk SSSR, vol.140, pp.326-329, 1961.

D. Thérien and T. Wilke, Over words, two variables are as powerful as one quantifier alternation, Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing, pp.234-240, 1998.

A. Weber and R. Klemm, Economy of description for single-valued transducers, STACS 94, 11th Annual Symposium on Theoretical Aspects of Computer Science, pp.607-618, 1994.