C. J. Anderson, N. Foster, A. Guha, J. Jeannin, D. Kozen et al., NetkAT, Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '14, pp.113-126, 2014.
DOI : 10.1145/2535838.2535862

A. Angus and D. Kozen, Kleene algebra with tests and program schematology, 2001.

V. M. Antimirov, Partial derivatives of regular expressions and finite automaton constructions, Theoretical Computer Science, vol.155, issue.2, pp.291-319, 1996.
DOI : 10.1016/0304-3975(95)00182-4

URL : http://doi.org/10.1016/0304-3975(95)00182-4

F. Bonchi and D. Pous, Checking NFA equivalence with bisimulations up to congruence, Proc. POPL, pp.457-468, 2013.
DOI : 10.1145/2429069.2429124

URL : https://hal.archives-ouvertes.fr/hal-00639716

T. Braibant and D. Pous, An Efficient Coq Tactic for Deciding Kleene Algebras, Proc. 1st ITP, pp.163-178, 2010.
DOI : 10.1007/978-3-642-14052-5_13

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.163.8920

J. Brotherston and A. Simpson, Sequent calculi for induction and infinite descent, Journal of Logic and Computation, vol.21, issue.6, pp.1177-1216, 2011.
DOI : 10.1093/logcom/exq052

K. Brünnler and T. Studer, Syntactic cut-elimination for common knowledge, Annals of Pure and Applied Logic, vol.160, issue.1, pp.82-95, 2009.
DOI : 10.1016/j.apal.2009.01.014

K. Brünnler and T. Studer, Syntactic cut-elimination for a fragment of the modal mu-calculus, Annals of Pure and Applied Logic, vol.163, issue.12, pp.1838-1853, 2012.
DOI : 10.1016/j.apal.2012.04.006

S. R. Buss, An introduction to proof theory. Handbook of proof theory, pp.1-78, 1998.
DOI : 10.1016/s0049-237x(98)80016-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.9979

W. Buszkowski, On Action Logic: Equational Theories of Action Algebras, Journal of Logic and Computation, vol.17, issue.1, pp.199-217, 2007.
DOI : 10.1093/logcom/exl036

J. H. Conway, Regular algebra and finite machines, 1971.

C. Dax, M. Hofmann, and M. Lange, A Proof System for the Linear Time ??-Calculus, Proc. FSTTCS, pp.273-284, 2006.
DOI : 10.1007/11944836_26

N. Dershowitz and Z. Manna, Proving termination with multiset orderings, Communications of the ACM, vol.22, issue.8, pp.465-476, 1979.
DOI : 10.1145/359138.359142

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.8728

A. Doumane, D. Baelde, L. Hirschi, and A. Saurin, Towards Completeness via Proof Search in the Linear Time ??-calculus, Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, pp.377-386, 2016.
DOI : 10.1006/inco.1999.2836

URL : https://hal.archives-ouvertes.fr/hal-01275289

J. Girard, Linear logic, Theoretical Computer Science, vol.50, issue.1, pp.1-102, 1987.
DOI : 10.1016/0304-3975(87)90045-4

URL : https://hal.archives-ouvertes.fr/inria-00075966

C. A. Hoare, B. Möller, G. Struth, and I. Wehrman, Concurrent Kleene Algebra, Proc. CONCUR, pp.399-414, 2009.
DOI : 10.1007/3-540-17906-2_31

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.979

J. E. Hopcroft and R. M. Karp, A linear algorithm for testing equivalence of finite automata, 1971.

P. Jipsen, From Semirings to Residuated Kleene Lattices, Studia Logica, vol.76, issue.2, pp.291-303, 2004.
DOI : 10.1023/B:STUD.0000032089.54776.63

S. C. Kleene, Representation of Events in Nerve Nets and Finite Automata, Automata Studies, pp.3-41, 1956.
DOI : 10.1515/9781400882618-002

D. Kozen, A completeness theorem for Kleene algebras and the algebra of regular events, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science, pp.214-225, 1991.
DOI : 10.1109/LICS.1991.151646

D. Kozen, On Action Algebras, Logic and Information Flow, pp.78-88, 1994.
DOI : 10.7146/dpb.v21i381.6613

D. Kozen, Kleene algebra with tests, ACM Transactions on Programming Languages and Systems, vol.19, issue.3, pp.427-443, 1997.
DOI : 10.1145/256167.256195

D. Kozen, On Hoare logic and Kleene algebra with tests, ACM Transactions on Computational Logic, vol.1, issue.1, pp.60-76, 2000.
DOI : 10.1145/343369.343378

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.9835

D. Kozen and M. Patron, Certification of Compiler Optimizations Using Kleene Algebra with Tests, Proc. CL2000, volume 1861 of LNAI, pp.568-582, 2000.
DOI : 10.1007/3-540-44957-4_38

A. Krauss and T. Nipkow, Proof Pearl: Regular Expression Equivalence and Relation Algebra, Journal of Automated Reasoning, vol.19, issue.1, pp.95-106, 2012.
DOI : 10.1017/S0956796808007090

D. Krob, A complete system of B-rational identities, Proc. ICALP, pp.60-73, 1990.
DOI : 10.1007/BFb0032022

URL : https://hal.archives-ouvertes.fr/hal-00017725

D. Krob, A complete system of B-rational identities, TCS, vol.89, issue.2, pp.207-343, 1991.
DOI : 10.1007/BFb0032022

URL : https://hal.archives-ouvertes.fr/hal-00017725

J. Lambek, The Mathematics of Sentence Structure, The American Mathematical Monthly, vol.65, issue.3, pp.154-170, 1958.
DOI : 10.2307/2310058

E. Palka, An infinitary sequent system for the equational theory of *-continuous action lattices, Fundam. Inform, pp.295-309, 2007.

D. Pous, Kleene Algebra with Tests and Coq Tools for while Programs, Proc. ITP, pp.180-196, 2013.
DOI : 10.1007/978-3-642-39634-2_15

URL : https://hal.archives-ouvertes.fr/hal-00785969

V. Pratt, Action logic and pure induction, Proc. JELIA, pp.97-120, 1990.
DOI : 10.1007/BFb0018436

URL : http://boole.stanford.edu/pub/jelia.pdf

K. Schütte, Proof Theory. Grundlehren der mathematischen Wissenschaften 225 Translation of Beweistheorie, 1968.

C. Wurm, Kleene Algebras, Regular Languages and Substructural Logics, Proc. GandALF, EPTCS, pp.46-59, 2014.
DOI : 10.4204/EPTCS.161.7

URL : http://arxiv.org/abs/1408.5956