A. Abboud, K. Censor-hillel, and S. Khoury, Near-linear lower bounds for distributed distance computations, even in sparse networks, Distributed Computing -30th International Symposium, DISC 2016, pp.29-42, 2016.

Y. Afek, S. Kutten, and M. Yung, The local detection paradigm and its application to self-stabilization, Theor. Comput. Sci, vol.186, issue.1-2, pp.286-287, 1997.

H. Arfaoui and P. Fraigniaud, What can be computed without communications? SIGACT News, vol.45, pp.82-104, 2014.

H. Arfaoui, P. Fraigniaud, and A. Pelc, Local decision and verification with bounded-size outputs, 15th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pp.133-147, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00922700

H. Arfaoui, P. Fraigniaud, D. Ilcinkas, and F. Mathieu, Distributedly testing cycle-freeness, 40th International Workshop on GraphTheoretic Concepts in Computer Science (WG), pp.15-28, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01084297

H. Attiya and J. Welch, Distributed Computing: Fundamentals, Simulations, and Advanced Topics, 2004.

B. Awerbuch, B. Patt-shamir, and G. Varghese, Self-stabilization by local checking and correction (extended abstract), 32nd Symposium on Foundations of Computer Science (FOCS), pp.268-277, 1991.

L. Babai, P. Frankl, and J. Simon, Complexity classes in communication complexity theory, Proc. 27th Annual Symposium on Foundations of Computer Science (FOCS 1986), pp.337-347, 1986.

A. Balliu and P. Fraigniaud, Certification of compact low-stretch routing schemes, 31st International Symposium on Distributed Computing, vol.6, pp.1-6, 2017.

A. Balliu, D. Gianlorenzo, P. Angelo, D. Fraigniaud, and . Olivetti, What can be verified locally?, 34th Symposium on Theoretical Aspects of Computer Science, STACS 2017, vol.8, pp.1-8, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01964764

A. Balliu, J. Hirvonen, J. H. Korhonen, T. Lempiäinen, D. Olivetti et al., New classes of distributed time complexity, Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, pp.1307-1318, 2018.

E. Bampas and D. Ilcinkas, On mobile agent verifiable problems, 12th Latin American Symposium on Theoretical Informatics (LATIN), pp.123-137, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01323114

J. Bang, -. Jensen, and G. Gutin, Digraphs -theory, algorithms and applications, 2002.

M. Baruch, P. Fraigniaud, and B. Patt-shamir, Randomized prooflabeling schemes, ACM Symposium on Principles of Distributed Computing (PODC), pp.315-324, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01247352

F. Becker, A. Kosowski, M. Matamala, N. Nisse, I. Rapaport et al., Allowing each node to communicate only once in a distributed system: shared whiteboard models, Distributed Computing, vol.28, issue.3, pp.189-200, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00704200

M. Bienkowski, L. Gasieniec, M. Klonowski, M. Korzeniowski, B. Mans et al., Distributed alarming in the on-duty and off-duty models, IEEE/ACM Trans. Netw, vol.24, issue.1, pp.218-230, 2016.

L. Blin and P. Fraigniaud, Space-optimal time-efficient silent selfstabilizing constructions of constrained spanning trees, 35th IEEE International Conference on Distributed Computing Systems (ICDCS), pp.589-598, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01247340

L. Blin, P. Fraigniaud, and B. Patt-shamir, On proof-labeling schemes versus silent self-stabilizing algorithms, 16th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS), pp.18-32, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01102123

L. Hans, M. Bodlaender, S. Cygan, J. Kratsch, and . Nederlof, Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth, Inf. Comput, vol.243, pp.86-111, 2015.

B. Bonakdarpour, P. Fraigniaud, S. Rajsbaum, D. A. Rosenblueth, and C. Travers, Decentralized asynchronous crash-resilient runtime verification, 27th International Conference on Concurrency Theory, vol.16, pp.1-16, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01423646

Z. Brakerski and B. Patt-shamir, Distributed discovery of large nearcliques, Distributed Computing, vol.24, issue.2, pp.79-89, 2011.

K. Censor-hillel, P. Kaski, J. H. Korhonen, C. Lenzen, A. Paz et al., Algebraic methods in the congested clique, ACM Symposium on Principles of Distributed Computing (PODC), pp.143-152, 2015.

K. Censor-hillel, E. Fischer, G. Schwartzman, and Y. Vasudev, Fast distributed algorithms for testing graph properties, Distributed Computing -30th International Symposium, DISC 2016, pp.43-56, 2016.

K. Censor-hillel, A. Paz, and M. Perry, Approximate proof-labeling schemes, Structural Information and Communication Complexity -24th International Colloquium, pp.71-89, 2017.

Y. Chang, T. Kopelowitz, and S. Pettie, An exponential separation between randomized and deterministic complexity in the LOCAL model, IEEE 57th Annual Symposium on Foundations of Computer Science, FOCS 2016, pp.615-624, 2016.

H. Thomas, C. E. Cormen, R. L. Leiserson, C. Rivest, and . Stein, Introduction to Algorithms, 2009.

A. Das-sarma, S. Holzer, L. Kor, A. Korman, D. Nanongkai et al., Distributed verification and hardness of distributed approximation, SIAM J. Comput, vol.41, issue.5, pp.1235-1265, 2012.

D. Dolev, C. Lenzen, and S. Peled, tri, tri again": Finding triangles and small subgraphs in a distributed setting -(extended abstract), 26th International Symposium on Distributed Computing (DISC), pp.195-209, 2012.

M. Elkin, H. Klauck, D. Nanongkai, and G. Pandurangan, Can quantum communication speed up distributed computation?, ACM Symposium on Principles of Distributed Computing, PODC '14, pp.166-175, 2014.

Y. Emek, C. Pfister, J. Seidel, and R. Wattenhofer, Anonymous networks: randomization = 2-hop coloring, ACM Symposium on Principles of Distributed Computing (PODC), pp.96-105, 2014.

Y. Emek, J. Seidel, and R. Wattenhofer, Computability in anonymous networks: Revocable vs. irrecovable outputs, Automata, Languages, and Programming -41st International Colloquium, ICALP 2014, Copenhagen, pp.183-195, 2014.

G. Even, M. Medina, and D. Ron, Best of two local models: Local centralized and local distributed algorithms, 2014.

G. Even, O. Fischer, P. Fraigniaud, T. Gonen, R. Levi et al., Three notes on distributed property testing, 31st International Symposium on Distributed Computing (DISC), 2017.
URL : https://hal.archives-ouvertes.fr/hal-01674664

L. Feuilloley, How long it takes for an ordinary node with an ordinary ID to output?, Structural Information and Communication Complexity -24th International Colloquium, pp.263-282, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02076161

L. Feuilloley and P. Fraigniaud, Randomized local network computing, 27th ACM on Symposium on Parallelism in Algorithms and Architectures (SPAA), pp.340-349, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01247357

L. Feuilloley and P. Fraigniaud, Survey of distributed decision, url: bulletin.eatcs.org link, vol.119, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01331880

L. Feuilloley and P. Fraigniaud, Error-sensitive proof-labeling schemes, 31st International Symposium on Distributed Computing, vol.16, pp.1-16, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01674660

L. Feuilloley and M. Habib, Graph classes and forbidden patterns on three vertices, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01958194

L. Feuilloley and J. Hirvonen, Local verification of global proofs, DISC 2018, 2018.

L. Feuilloley, J. Hirvonen, and J. Suomela, Locally optimal load balancing, 29th International Symposium, DISC 2015, pp.544-558, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01207214

L. Feuilloley, P. Fraigniaud, and J. Hirvonen, A hierarchy of local decision, 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, vol.118, pp.1-118, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01423644

L. Feuilloley, P. Fraigniaud, J. Hirvonen, A. Paz, and M. Perry, Redundancy in distributed proofs, DISC 2018, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01964771

F. E. Fich and E. Ruppert, Hundreds of impossibility results for distributed computing, Distributed Computing, vol.16, issue.2-3, pp.121-163, 2003.

H. Fichtenberger and Y. Vasudev, A two-sided error distributed property tester for conductance, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, vol.19, pp.1-19, 2018.

P. Flocchini, G. Prencipe, and N. Santoro, Distributed Computing by Oblivious Mobile Robots, 2012.

K. Förster, T. Luedi, J. Seidel, and R. Wattenhofer, Local checkability, no strings attached, 17th International Conference on Distributed Computing and Networking (ICDCN), p.21, 2016.

P. Fraigniaud, Locality in distributed graph algorithms, Encyclopedia of Algorithms, pp.1143-1148, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01423632

P. Fraigniaud and D. Olivetti, Distributed detection of cycles, Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2017, pp.153-162, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01674646

P. Fraigniaud and A. Pelc, Decidability classes for mobile agents computing, 10th Latin American Symposium on Theoretical Informatics (LATIN), pp.362-374, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01674623

P. Fraigniaud, C. Gavoille, D. Ilcinkas, and A. Pelc, Distributed computing with advice: information sensitivity of graph coloring, Distributed Computing, vol.21, issue.6, pp.395-403, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00339878

P. Fraigniaud, A. Korman, and D. Peleg, Local distributed decision, IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, pp.708-717, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00912561

P. Fraigniaud, M. Magnús, A. Halldórsson, and . Korman, On the impact of identifiers on local decision, 16th International Conference Principles of Distributed Systems (OPODIS), pp.224-238, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01241093

P. Fraigniaud, M. Göös, A. Korman, and J. Suomela, What can be decided locally without identifiers, ACM Symposium on Principles of Distributed Computing (PODC), pp.157-165, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00912527

P. Fraigniaud, A. Korman, and D. Peleg, Towards a complexity theory for local distributed computing, J. ACM, vol.60, issue.5, p.35, 2013.

P. Fraigniaud, S. Rajsbaum, and C. Travers, Locality and checkability in wait-free computing, Distributed Computing, vol.26, issue.4, pp.223-242, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00605244

P. Fraigniaud, M. Göös, A. Korman, M. Parter, and D. Peleg, Randomized distributed decision. Distributed Computing, vol.27, pp.419-434, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01093255

P. Fraigniaud, S. Rajsbaum, M. Roy, and C. Travers, The opinion number of set-agreement, 18th International Conference on the Principles of Distributed Systems (OPODIS), pp.155-170, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01073578

P. Fraigniaud, S. Rajsbaum, and C. Travers, On the number of opinions needed for fault-tolerant run-time monitoring in distributed systems, 5th International Conference on Runtime Verification (RV), pp.92-107, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01102121

P. Fraigniaud, J. Hirvonen, and J. Suomela, Node labels in local decision, 22nd International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp.31-45, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01247355

P. Fraigniaud, S. Rajsbaum, and C. Travers, Minimizing the number of opinions for fault-tolerant distributed decision using well-quasi orderings, 12th Latin American Symposium on Theoretical Informatics (LATIN), pp.497-508, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01423679

P. Fraigniaud, S. Rajsbaum, C. Travers, P. Kuznetsov, and T. Rieutord, Perfect failure detection with very few bits, Stabilization, Safety, and Security of Distributed Systems -18th International Symposium, pp.154-169, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01365304

P. Fraigniaud, I. Rapaport, V. Salo, and I. Todinca, Distributed testing of excluded subgraphs, Distributed Computing -30th International Symposium, pp.342-356, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01423633

R. G. Gallager, P. A. Humblet, and P. M. Spira, A distributed algorithm for minimum-weight spanning trees, ACM Trans. Program. Lang. Syst, vol.5, issue.1, pp.66-77, 1983.

O. Goldreich, A brief introduction to property testing, Studies in Complexity and Cryptography -Miscellanea on the Interplay between Randomness and Computation, number 6650 in LNCS, pp.465-469, 2011.

O. Goldreich, Introduction to testing graph properties, Studies in Complexity and Cryptography -Miscellanea on the Interplay between Randomness and Computation, number 6650 in LNCS, pp.470-506, 2011.

M. Göös and J. Suomela, Locally checkable proofs, 30th ACM Symposium on Principles of Distributed Computing (PODC), pp.159-168, 2011.

M. Göös and J. Suomela, Locally checkable proofs in distributed computing, Theory of Computing, vol.12, issue.19, pp.1-33, 2016.

M. Göös, J. Hirvonen, R. Levi, M. Medina, and J. Suomela, Nonlocal probes do not help with many graph problems, Distributed Computing -30th International Symposium, DISC 2016, pp.201-214, 2016.

T. Gur and R. D. Rothblum, Non-interactive proofs of proximity, Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, pp.133-142, 2015.

T. Gur and R. D. Rothblum, Non-interactive proofs of proximity, Computational Complexity, vol.27, issue.1, pp.99-207, 2018.

M. Magnús, T. Halldórsson, and . Tonoyan, How well can graphs represent wireless interference?, Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing, STOC 2015, pp.635-644, 2015.

G. Itkis and L. A. Levin, Fast and lean self-stabilizing asynchronous protocols, 35th Annual Symposium on Foundations of Computer Science (FOCS), pp.226-239, 1994.

J. Kari, M. Matamala, I. Rapaport, and V. Salo, Solving the induced subgraph problem in the randomized multiparty simultaneous messages model, 22nd International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp.370-384, 2015.

H. Klauck, D. Nanongkai, G. Pandurangan, and P. Robinson, Distributed computation of large-scale graph problems, Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, pp.391-410, 2015.

L. Kor, A. Korman, and D. Peleg, Tight bounds for distributed MST verification, 28th International Symposium on Theoretical Aspects of Computer Science (STACS), pp.69-80, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00573623

L. Kor, A. Korman, and D. Peleg, Tight bounds for distributed minimum-weight spanning tree verification, Theory Comput. Syst, vol.53, issue.2, pp.318-340, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01241088

H. Janne, J. Korhonen, and . Rybicki, Deterministic subgraph detection in broadcast CONGEST, 21st International Conference on Principles of Distributed Systems, vol.4, pp.1-4, 2017.

H. Janne, J. Korhonen, and . Suomela, Brief announcement: Towards a complexity theory for the congested clique, 31st International Symposium on Distributed Computing, vol.55, pp.1-55, 2017.

A. Korman and S. Kutten, Distributed verification of minimum spanning trees, Distributed Computing, vol.20, issue.4, pp.253-266, 2007.

A. Korman, S. Kutten, and D. Peleg, Proof labeling schemes

A. Korman, S. Kutten, and D. Peleg, Proof labeling schemes, Proceedings of the Twenty-Fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, pp.9-18, 2005.

A. Korman, S. Kutten, and D. Peleg, Proof labeling schemes, Distributed Computing, vol.22, issue.4, pp.215-233, 2010.

A. Korman, S. Kutten, and T. Masuzawa, Fast and compact selfstabilizing verification, computation, and fault detection of an MST, Distributed Computing, vol.28, issue.4, pp.253-295, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01240211

E. Koutsoupias and C. H. Papadimitriou, Worst-case equilibria, Computer Science Review, vol.3, issue.2, pp.65-69, 2009.

F. Kuhn, The price of locality: exploring the complexity of distributed coordination primitives, 2005.

E. Kushilevitz and N. Nisan, Communication complexity, 1997.

N. Linial, Locality in distributed graph algorithms, SIAM J. Comput, vol.21, issue.1, pp.193-201, 1992.

L. Lovász and K. Vesztergombi, Non-deterministic graph property testing, Combinatorics, Probability & Computing, vol.22, issue.5, pp.749-762, 2013.

M. Naor and L. J. Stockmeyer, What can be computed locally?, SIAM J. Comput, vol.24, issue.6, pp.1259-1277, 1995.

R. Ostrovsky, M. Perry, and W. Rosenbaum, Space-time tradeoffs for distributed verification, Structural Information and Communication Complexity -24th International Colloquium, pp.53-70, 2017.

G. Pandurangan, P. Robinson, and M. Scquizzato, Fast distributed algorithms for connectivity and MST in large graphs, Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2016, Asilomar State Beach, pp.429-438, 2016.

C. H. Papadimitriou, Algorithms, games, and the internet, Proceedings on 33rd Annual ACM Symposium on Theory of Computing, pp.749-753, 2001.

M. Parnas and D. Ron, Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms, Theor. Comput. Sci, vol.381, issue.1-3, pp.183-196, 2007.

B. Patt, -. Shamir, and M. Perry, Proof-labeling schemes: Broadcast, unicast and in between, Stabilization, Safety, and Security of Distributed Systems -19th International Symposium, pp.1-17, 2017.

D. Peleg, Distributed Computing: A Locality-Sensitive Approach. SIAM, 2000.

D. Peleg and V. Rubinovich, A near-tight lower bound on the time complexity of distributed MST construction, 40th Symp. on Foundations of Computer Science (FOCS), pp.253-261, 1999.

F. Reiter, Distributed graph automata, 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pp.192-201, 2015.

F. Reiter, Distributed automata and logic, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01953461

M. Schaefer, Deciding the Vapnik-Cervonenkis dimension in ? p, p.3

, J. Comput. Syst. Sci, vol.58, issue.1, pp.177-182, 1999.

M. Schaefer and C. Umans, Completeness in the polynomial-time hierarchy: A compendium, SIGACT news, vol.33, issue.3, pp.32-49, 2002.

S. Schmid and J. Suomela, Exploiting locality in distributed SDN control, Proceedings of the Second ACM Workshop on Hot Topics in Software Defined Networking (HotSDN), pp.121-126, 2013.

T. Schwentick and K. Barthelmann, Local normal forms for first-order logic with applications to games and automata, Discrete Mathematics & Theoretical Computer Science, vol.3, issue.3, pp.109-124, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00958930

J. Suomela, Survey of local algorithms, ACM Comput. Surv, vol.45, issue.2, p.24, 2013.

A. Yao, Some complexity questions related to distributive computing, 11h Symp. on Theory of Computing (STOC), pp.209-213, 1979.