|. =. and |. |e|, 2. every T i has one state, 3. there is a bijection f : H ? P aths * (V ? ), 4. the restriction of f to H w? is a bijection between H w? and P lays * , and 5. for every (2 AP , ?)-tree t ? H, for every node x ? t, for every state formula ? ? mL , t, |= ? iff f (t), f (x) |= ?
URL : https://hal.archives-ouvertes.fr/hal-01317661

=. Ap-\-{inc, L. Good, R. , and ?. , C(j) be a TM configuration of length at least 2. A TM configuration code (for C) is a word over ?} of the form code = ? · bl 0 . . . bl j · ? satisfying the following: ? ? = $ if C is not accepting and ? = $ acc otherwise; ? for all 0 ? i ? j, bl i is a k-block whose content is C(i)

L. Bibliography-de-alfaro and T. A. Henzinger, Concurrent omega-regular games, pp.141-154, 2000.

R. Alur, T. A. Henzinger, and O. Kupferman, Alternating-time temporal logic, Journal of the ACM, vol.49, issue.5, pp.672-713, 2002.
DOI : 10.1145/585265.585270

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.5461

G. Aucher, Infinite Games in Epistemic Temporal Logic via Supervisory Control Theory, 2013.

G. Aucher and A. Herzig, Exploring the Power of Converse Events, Dynamic formal epistemology, pp.51-74, 2011.
DOI : 10.1007/978-94-007-0074-1_4

URL : https://hal.archives-ouvertes.fr/hal-00557002

G. Aucher, B. Maubert, and F. Schwarzentruber, Tableau Method and NEXPTIME-Completeness of DEL-Sequents, Methods for Modalities (M4M), pp.17-30, 2011.
DOI : 10.1016/j.entcs.2011.10.003

URL : https://hal.archives-ouvertes.fr/inria-00627642

G. Aucher, B. Maubert, and F. Schwarzentruber, Generalized DEL-Sequents, Generalized DEL- Sequents. in JELIA, pp.54-66, 2012.
DOI : 10.1016/j.entcs.2011.10.015

URL : https://hal.archives-ouvertes.fr/hal-00856472

A. Baltag, L. S. Moss, and S. Solecki, The Logic of Public Announcements, Common Knowledge, and Private Suspicions, Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge, pp.43-56, 1998.
DOI : 10.1007/978-3-319-20451-2_38

W. Bekker and V. Goranko, Symbolic Model Checking of Tense Logics on Rational Kripke Models, ILC, pp.2-20, 2007.
DOI : 10.1007/978-3-642-03092-5_2

J. Van-benthem, Games in Dynamic-Epistemic Logic, The Philosophy of Jaakko Hintikka, pp.219-248, 2001.
DOI : 10.1111/1467-8586.00133

J. Van-benthem, Logical dynamics of information and interaction, 2011.
DOI : 10.1017/CBO9780511974533

J. Van-benthem, J. Gerbrandy, T. Hoshi, and E. Pacuit, Merging frameworks for interaction, Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge , TARK '07, pp.491-526, 2009.
DOI : 10.1145/1324249.1324262

J. Van-benthem and F. Liu, Diversity of Logical Agents in Games, Philosophia Scientae, vol.8, issue.8-2, pp.163-178, 2004.
DOI : 10.4000/philosophiascientiae.571

J. Bernet, D. Janin, and I. Walukiewicz, Permissive strategies: from parity games to safety games, RAIRO - Theoretical Informatics and Applications, vol.36, issue.3, pp.261-275, 2002.
DOI : 10.1051/ita:2002013

URL : https://hal.archives-ouvertes.fr/hal-00306411

J. Berstel, Transductions and context-free languages, Teubner Stuttgart), vol.4, 1979.
DOI : 10.1007/978-3-663-09367-1

URL : https://hal.archives-ouvertes.fr/hal-00619779

D. Berwanger, K. Chatterjee, M. D. Wulf, L. Doyen, and T. A. Henzinger, Strategy construction for parity games with imperfect information, Information and Computation, vol.208, issue.10, pp.1206-1220, 2010.
DOI : 10.1016/j.ic.2009.09.006

D. Berwanger and L. Doyen, On the power of imperfect information, FSTTCS of LIPIcs, pp.73-82, 2008.

D. Berwanger and L. Kaiser, Information Tracking in Games on Graphs, Journal of Logic, Language and Information, vol.90, issue.4, pp.395-412, 2010.
DOI : 10.1007/s10849-009-9115-8

D. Berwanger, L. Kaiser, and S. Leßenich, Solving Counter Parity Games, MFCS, pp.160-171, 2012.
DOI : 10.1007/978-3-642-32589-2_17

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.349.9961

A. Blumensath and E. Grädel, Automatic structures, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332), pp.51-62, 2000.
DOI : 10.1109/LICS.2000.855755

A. Blumensath and E. Grädel, Finite Presentations of Infinite Structures: Automata and Interpretations, Theory of Computing Systems, vol.37, issue.6, pp.641-674, 2004.
DOI : 10.1007/s00224-004-1133-y

M. Bojanczyk, Two-way alternating automata and finite models, ICALP, 2002.

T. Bolander and M. B. Andersen, Epistemic planning for singleand multi-agent systems, Journal of Applied Non-Classical Logics, vol.3, issue.3, pp.9-34, 2011.
DOI : 10.1016/0010-0277(83)90004-5

A. K. Chandra, D. Kozen, and L. J. Stockmeyer, Alternation, Journal of the ACM, vol.28, issue.1, pp.114-133, 1981.
DOI : 10.1145/322234.322243

K. Chatterjee, L. Doyen, T. A. Henzinger, and J. F. Raskin, Algorithms for Omega-Regular Games with Imperfect Information, CSL, pp.287-302, 2006.
DOI : 10.1007/11874683_19

E. M. Clarke and E. A. Emerson, Design and synthesis of synchronization skeletons using branching time temporal logic, Logic of Programs, pp.52-71, 1981.
DOI : 10.1007/BFb0025774

C. Dégremont, B. Löwe, and A. Witzel, The synchronicity of dynamic epistemic logic. in TARK, pp.145-152, 2011.

C. Dima, Revisiting Satisfiability and Model-Checking for CTLK with Synchrony and Perfect Recall, CLIMA, pp.117-131, 2008.
DOI : 10.1109/CSFW.2004.1310747

C. Dima, C. Enea, and D. P. Guelev, Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect Information, Perfect Recall and Communicating Coalitions, Electronic Proceedings in Theoretical Computer Science, pp.10-4204, 2010.
DOI : 10.4204/EPTCS.25.12

H. Van-ditmarsch and B. Kooi, Semantic results for ontic and epistemic change. Logic and the Foundations of Game and Decision Theory, p.87, 2006.

S. Dziembowski, M. Jurdzinski, and I. Walukiewicz, How much memory is needed to win infinite games? in LICS, pp.99-11010, 1997.

J. Van-eijck, Guarded actions, 2004.

E. A. Emerson, Temporal and modal logic. in Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics, pp.995-1072, 1990.

E. A. Emerson and J. Y. Halpern, "Sometimes" and "not never" revisited, Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '83, pp.127-140, 1983.
DOI : 10.1145/567067.567081

E. A. Emerson and C. L. Lei, Efficient model checking in fragments of the propositional mu-calculus (extended abstract), pp.267-278, 1986.

F. Engström, Generalized Quantifiers in Dependence Logic, Journal of Logic, Language and Information, vol.13, issue.4, pp.299-324, 2012.
DOI : 10.1007/s10849-012-9162-4

R. Fagin, J. Halpern, and M. Vardi, A model-theoretic analysis of knowledge, Journal of the ACM, vol.38, issue.2, pp.382-428, 1991.
DOI : 10.1145/103516.128680

C. Frougny and J. Sakarovitch, Synchronized rational relations of finite and infinite words, Theoretical Computer Science, vol.108, issue.1, pp.45-82, 1993.
DOI : 10.1016/0304-3975(93)90230-Q

P. Galliani, Inclusion and exclusion dependencies in team semantics ??? On some logics of imperfect information, Annals of Pure and Applied Logic, vol.163, issue.1, pp.68-84, 2012.
DOI : 10.1016/j.apal.2011.08.005

M. Ghallab, D. S. Nau, and P. Traverso, Automated planning -theory and practice, 2004.

E. Grädel, Model-checking games for logics of imperfect information, Theoretical Computer Science, vol.493, pp.2-14, 2013.
DOI : 10.1016/j.tcs.2012.10.033

E. Grädel, W. Thomas, and T. Wilke, Automata, Logics, and Infinite Games: A Guide to Current Research [outcome of a Dagstuhl seminar, Lecture Notes in Computer Science, vol.2500, 2001.
DOI : 10.1007/3-540-36387-4

E. Grädel and J. A. Väänänen, Dependence and Independence, Studia Logica, vol.18, issue.3, pp.399-410, 2013.
DOI : 10.1007/s11225-013-9479-2

J. Y. Halpern and M. Y. Vardi, The complexity of reasoning about knowledge and time. I. Lower bounds, Journal of Computer and System Sciences, vol.38, issue.1, pp.195-237, 1989.
DOI : 10.1016/0022-0000(89)90039-1

L. Henkin, Some remarks on infinitely long formulas, Infinitistic Methods, pp.167-183, 1961.

J. Hintikka, Knowledge and belief, 1962.

J. Hintikka and G. Sandu, Informational independence as a semantical phenomenon, Studies in Logic and the Foundations of Mathematics, pp.571-589, 1989.

W. Hodges, Compositional semantics for a language of imperfect information, Logic Journal of IGPL, vol.5, issue.4, pp.539-563, 1997.
DOI : 10.1093/jigpal/5.4.539

W. Van-der-hoek and M. Wooldridge, Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications, Studia Logica, vol.75, issue.1, pp.125-15710, 2003.
DOI : 10.1023/A:1026185103185

J. E. Hopcroft, R. Motwani, and J. D. Ullman, Introduction to automata theory , languages, and computation -international edition, 2003.

T. Hoshi and A. Yap, Dynamic epistemic logic with branching temporal structures, Synthese, vol.151, issue.2, pp.259-281, 2009.
DOI : 10.1007/s11229-009-9552-6

R. Hossley and C. Rackoff, The emptiness problem for automata on infinite trees, 13th Annual Symposium on Switching and Automata Theory (swat 1972), pp.121-124, 1972.
DOI : 10.1109/SWAT.1972.28

W. Jamroga and W. Van-der-hoek, Agents that know how to play, Fundam. Inform, vol.63, issue.2-3, pp.185-219, 2004.

J. H. Johnson, Rational equivalence relations, Theoretical Computer Science, vol.47, issue.3, pp.39-60, 1986.
DOI : 10.1016/0304-3975(86)90132-5

P. C. Kanellakis and S. A. Smolka, CCS expressions, finite state processes, and three problems of equivalence, Information and Computation, vol.86, issue.1, pp.43-68, 1990.
DOI : 10.1016/0890-5401(90)90025-D

B. Khoussainov and A. Nerode, Automatic presentations of structures, LCC, pp.367-392, 1994.
DOI : 10.1007/3-540-60178-3_93

B. Khoussainov, A. Nies, S. Rubin, and F. Stephan, Automatic structures: Richness and limitations, Logical Methods in Computer Science, vol.3, issue.2, 2007.
DOI : 10.2168/lmcs-3(2:2)2007

URL : http://arxiv.org/abs/cs/0703064

D. Kozen, Results on the propositional ??-calculus, Theoretical Computer Science, vol.27, issue.3, pp.333-354, 1983.
DOI : 10.1016/0304-3975(82)90125-6

O. Kupferman and M. Y. Vardi, Module checking revisited, Module checking revisited. in CAV, pp.36-47, 1997.
DOI : 10.1007/3-540-63166-6_7

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.108.8199

O. Kupferman, M. Y. Vardi, and P. Wolper, An automata-theoretic approach to branching-time model checking, Journal of the ACM, vol.47, issue.2, pp.312-360, 2000.
DOI : 10.1145/333979.333987

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.3149

O. Kupferman, M. Y. Vardi, and P. Wolper, Module Checking, Information and Computation, vol.164, issue.2, pp.322-344, 2001.
DOI : 10.1006/inco.2000.2893

R. E. Ladner and J. H. Reif, The Logic of Distributed Protocols. in TARK, pp.207-222, 1986.

D. Lehmann, Knowledge, common knowledge and related puzzles (Extended Summary), Proceedings of the third annual ACM symposium on Principles of distributed computing , PODC '84, pp.62-67, 1984.
DOI : 10.1145/800222.806736

F. Liu, Diversity of Agents and Their Interaction, Journal of Logic, Language and Information, vol.17, issue.2, pp.23-53, 2009.
DOI : 10.1007/s10849-008-9072-7

C. Löding, Automata on infinite trees. in preliminary version for the handbook Automata: from Mathematics to Applications, 2014.

B. Löwe, E. Pacuit, and A. Witzel, DEL Planning and Some Tractable Cases, DEL planning and some tractable cases. in LORI, pp.179-192, 2011.
DOI : 10.1016/j.ic.2006.04.006

B. Maubert and S. Pinchinat, Games with Opacity Condition, Reachability Problems, pp.166-175, 2009.
DOI : 10.1016/S0022-0000(70)80006-X

URL : https://hal.archives-ouvertes.fr/inria-00555749

B. Maubert and S. Pinchinat, Uniform strategies. in LOFT 2012, 10th Conference on Logic and the Foundations of Game and Decision Theory, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00760370

B. Maubert and S. Pinchinat, Jumping automata for uniform strategies, Proceedings of the 33rd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS'13) Leibniz International Proceedings in Informatics, pp.287-298, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01098741

B. Maubert and S. Pinchinat, A GENERAL NOTION OF UNIFORM STRATEGIES, International Game Theory Review, vol.16, issue.01, pp.10-1142, 2014.
DOI : 10.1142/S0219198914400040

URL : https://hal.archives-ouvertes.fr/hal-01098738

B. Maubert, S. Pinchinat, and L. Bozzelli, Opacity Issues in Games with Imperfect Information, GandALF, pp.87-101, 2011.
DOI : 10.4204/EPTCS.54.7

URL : https://hal.archives-ouvertes.fr/inria-00630077

B. Maubert, S. Pinchinat, and L. Bozzelli, The Complexity of Synthesizing Uniform Strategies, Proceedings 1st International Workshop on Strategic Reasoning, pp.115-122, 2013.
DOI : 10.4204/EPTCS.112.17

URL : https://hal.archives-ouvertes.fr/hal-01098745

R. Mcnaughton, Infinite games played on finite graphs, Annals of Pure and Applied Logic, vol.65, issue.2, pp.149-184, 1993.
DOI : 10.1016/0168-0072(93)90036-D

A. Meduna and P. Zemek, JUMPING FINITE AUTOMATA, International Journal of Foundations of Computer Science, vol.23, issue.07, pp.1555-1578, 2012.
DOI : 10.1142/S0129054112500244

R. Van-der-meyden and N. V. Shilov, Model Checking Knowledge and Time in Systems with Perfect Recall, FSTTCS, pp.432-445, 1999.
DOI : 10.1007/3-540-46691-6_35

R. Van-der-meyden and M. Y. Vardi, Synthesis from knowledge-based specifications, CONCUR'98 Concurrency Theory, pp.34-49, 1998.
DOI : 10.1007/BFb0055614

R. Van-der-meyden and T. Wilke, Synthesis of Distributed Systems from Knowledge-Based Specifications, in CONCUR Lecture Notes in Computer Science, vol.3653, pp.562-576, 2005.
DOI : 10.1007/11539452_42

C. Morvan, On Rational Graphs, FoSSaCS, pp.252-266, 2000.
DOI : 10.1007/3-540-46432-8_17

URL : https://hal.archives-ouvertes.fr/hal-00620062

C. Morvan and C. Rispal, Families of automata characterizing context-sensitive languages, Acta Informatica, vol.25, issue.4-5, pp.293-314, 2005.
DOI : 10.1007/s00236-004-0160-0

URL : https://hal.archives-ouvertes.fr/inria-00525422

D. E. Muller and P. E. Schupp, Alternating automata on infinite trees, Theoretical Computer Science, vol.54, issue.2-3, pp.267-276, 1987.
DOI : 10.1016/0304-3975(87)90133-2

D. E. Muller and P. E. Schupp, Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra, Theoretical Computer Science, vol.141, issue.1-2, pp.69-107, 1995.
DOI : 10.1016/0304-3975(94)00214-4

E. Pacuit, Some comments on history based structures, Journal of Applied Logic, vol.5, issue.4, pp.613-624, 2007.
DOI : 10.1016/j.jal.2006.03.012

E. Pacuit and J. Van-benthem, The tree of knowledge in action: Towards a common perspective, Proceedings of Advances in Modal Logic Volume, pp.87-106, 2006.

R. Parikh and R. Ramanujam, Distributed processes and the logic of knowledge, Logic of Programs, pp.256-268, 1985.
DOI : 10.1007/3-540-15648-8_21

R. Parikh and R. Ramanujam, A knowledge based semantics of messages, Journal of Logic, Language and Information, vol.12, issue.4, pp.453-467, 2003.
DOI : 10.1023/A:1025007018583

G. Peterson, J. H. Reif, and S. Azhar, Lower bounds for multiplayer noncooperative games of incomplete information, Computers & Mathematics with Applications, vol.41, issue.7-8, pp.957-992, 2001.
DOI : 10.1016/S0898-1221(00)00333-3

M. Piccione and A. Rubinstein, The Absent-Minded Driver's Paradox: Synthesis and Responses, Games and Economic Behavior, vol.20, issue.1, pp.121-130, 1997.
DOI : 10.1006/game.1997.0579

N. Piterman and M. Y. Vardi, Global Model-Checking of Infinite-State Systems, CAV, pp.387-400, 2004.
DOI : 10.1007/978-3-540-27813-9_30

A. Pnueli, The temporal logic of programs, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977), pp.46-57, 1977.
DOI : 10.1109/SFCS.1977.32

A. Pnueli and R. Rosner, On the synthesis of an asynchronous reactive module, Proc. 16th Int. Coll. on Automata, Languages and Programming, ICALP'89, pp.652-671, 1989.
DOI : 10.1007/BFb0035790

B. Puchala, Asynchronous Omega-Regular Games with Partial Information, MFCS, pp.592-603, 2010.
DOI : 10.1007/978-3-642-15155-2_52

P. J. Ramadge and W. M. Wonham, Supervisory Control of a Class of Discrete Event Processes, SIAM Journal on Control and Optimization, vol.25, issue.1, pp.206-230, 1987.
DOI : 10.1137/0325013

J. H. Reif, The complexity of two-player games of incomplete information, Journal of Computer and System Sciences, vol.29, issue.2, pp.274-301, 1984.
DOI : 10.1016/0022-0000(84)90034-5

S. Riedweg and S. Pinchinat, Quantified Mu-Calculus for Control Synthesis, MFCS, pp.642-651, 2003.
DOI : 10.1007/978-3-540-45138-9_58

URL : https://hal.archives-ouvertes.fr/inria-00071793

J. Sato, A study of kripke style methods for some modal logic by gentzen's sequential method, Tech. Rep, 1977.

W. Thomas, Automata on infinite objects. in Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics, pp.133-192, 1990.

J. A. Väänänen, Dependence Logic -A New Approach to Independence Friendly Logic, 2007.

M. Y. Vardi, Alternating automata and program verification, Computer Science Today, pp.471-485, 1995.
DOI : 10.1007/BFb0015261

M. Y. Vardi, Reasoning about the past with two-way automata, ICALP, pp.628-641, 1998.
DOI : 10.1007/BFb0055090

M. Y. Vardi, From Church and Prior to PSL, 25 Years of Model Checking, pp.150-171, 2008.
DOI : 10.1007/978-3-540-69850-0_10

M. Y. Vardi and P. Wolper, Reasoning about Infinite Computations, Information and Computation, vol.115, issue.1, pp.1-37, 1994.
DOI : 10.1006/inco.1994.1092

Y. Wang and G. Aucher, An alternative axiomatization of DEL and its applications, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00856470

Q. Yu, X. Wen, and Y. Liu, Multi-agent epistemic explanatory diagnosis via reasoning about actions, IJCAI, pp.1183-1190, 2013.

W. Zielonka, Infinite games on finitely coloured graphs with applications to automata on infinite trees, Theoretical Computer Science, vol.200, issue.1-2, pp.135-183, 1998.
DOI : 10.1016/S0304-3975(98)00009-7