Z. S. Andraus, Automatic abstraction and verification of verilog models, Proceedings of the 41st annual conference on Design automation , DAC '04, 2004.
DOI : 10.1145/996566.996629

D. Babic and M. Musuvathi, Modular arithmetic decision procedure, 2005.

M. Barnett, B. E. Chang, R. Deline, B. Jacobs, and K. R. Leino, Boogie: A Modular Reusable Verifier for Object-Oriented Programs, Formal methods for Components and Objects, pp.364-387, 2006.
DOI : 10.1007/11804192_17

C. Barrett and C. Tinelli, CVC3, Proceedings of the 19 th International Conference on Computer Aided Verification (CAV '07), pp.298-302, 2007.
DOI : 10.1007/978-3-540-73368-3_34

F. Bobot, S. Conchon, E. Contejean, M. Iguernelala, A. Mahboubi et al., A simplex-based extension of fouriermotzkin for solving linear integer arithmetic, Automated Reasoning, pp.67-81, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00687640

F. Bobot, J. Filliâtre, C. Marché, and A. Paskevich, Shepherd your herd of provers, Boogie 2011: First International Workshop on Intermediate Verification Languages, pp.53-64, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00790310

M. Bozzano, R. Bruttomesso, A. Cimatti, A. Franzén, Z. Hanna et al., Encoding RTL Constructs for MathSAT: a Preliminary Report, Electronic Notes in Theoretical Computer Science, vol.144, issue.2, pp.3-14, 2006.
DOI : 10.1016/j.entcs.2005.12.001

C. W. Brown, QEPCAD B, ACM SIGSAM Bulletin, vol.37, issue.4, pp.97-108, 2003.
DOI : 10.1145/968708.968710

G. E. Collins, Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition, ACM SIGSAM Bulletin, vol.10, issue.1, pp.10-12, 1976.
DOI : 10.1145/1093390.1093393

S. Conchon, E. Contejean, and M. Iguernelala, Canonized Rewriting and Ground AC Completion Modulo Shostak Theories, 15th International Conference on Rewriting Techniques and Applications, pp.70-84, 2004.
DOI : 10.1145/357073.357079
URL : https://hal.archives-ouvertes.fr/hal-00777663

E. Contejean, C. Marché, A. P. Tomás, and X. Urbain, Mechanically Proving Termination Using Polynomial Interpretations, Journal of Automated Reasoning, vol.12, issue.1, pp.325-363, 2005.
DOI : 10.1007/s10817-005-9022-x
URL : https://hal.archives-ouvertes.fr/inria-00001167

L. M. De-moura and N. Bjørner, Model-based Theory Combination, Electronic Notes in Theoretical Computer Science, vol.198, issue.2, pp.37-49, 2008.
DOI : 10.1016/j.entcs.2008.04.079

L. M. De-moura and N. Bjørner, Z3: An efficient smt solver In Tools and Algorithms for the Construction and Analysis of Systems, 14th International Conference, pp.337-340, 2008.

B. Dutertre and L. D. Moura, The yices smt solver, 2006.

J. J. Fourier, Reported in: Analyse des travaux de l'Académie Royale des Sciences, pendant l'année 1824, Partie mathématique, Histoire de l'Académie Royale des Sciences de l, p.1827

M. Fränzle, C. Herde, T. Teige, S. Ratschan, and T. Schubert, Efficient solving of large non-linear arithmetic constraint systems with complex boolean structure, Journal on Satisfiability Boolean Modeling and Computation, vol.1, pp.209-236, 2007.

M. K. Ganai, Efficient decision procedure for bounded integer non-linear operations using smt (\ mathcal {LIA}) In Hardware and Software: Verification and Testing, 22] K. Gödel. ¨ Uber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, pp.68-83173, 1931.

T. Hickey, Q. Ju, and M. H. Van-emden, Interval arithmetic: From principles to implementation, Journal of the ACM, vol.48, issue.5, pp.1038-1068, 2001.
DOI : 10.1145/502102.502106

J. Hullot, Associative commutative pattern matching, Proc. 6th IJCAI, pp.406-412, 1979.

D. Jovanovic and L. M. De-moura, Solving Non-linear Arithmetic, Automated Reasoning -6th International Joint Conference, pp.339-354, 2012.
DOI : 10.1007/978-3-642-31365-3_27

J. Kanig, E. Schonberg, and C. Dross, Hi-Lite, Proceedings of the 2012 ACM conference on High integrity language technology, HILT '12, pp.27-34, 2012.
DOI : 10.1145/2402676.2402690

D. Kapur, Using Gr??bner bases to reason about geometry problems, Journal of Symbolic Computation, vol.2, issue.4, pp.399-408, 1986.
DOI : 10.1016/S0747-7171(86)80007-4

D. Kroening and O. Strichman, Decision Procedures: An Algorithmic Point of View, 2008.
DOI : 10.1007/978-3-662-50497-0

S. Krsti´ckrsti´c and S. Conchon, Canonization for disjoint unions of theories, Information and Computation, vol.199, issue.1-2, pp.87-106, 2005.
DOI : 10.1016/j.ic.2004.11.001

S. Krstic and A. Goel, Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL, Frontiers of Combining Systems Proceedings, pp.1-27, 2007.
DOI : 10.1007/978-3-540-74621-8_1

C. Marché, Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations, Journal of Symbolic Computation, vol.21, issue.3, pp.253-288, 1996.
DOI : 10.1006/jsco.1996.0011

Y. V. Matiyasevich, Enumerable sets are diophantine, Soviet Mathematics (Dokladi), vol.11, issue.2, pp.354-357, 1970.

R. Nieuwenhuis, A. Oliveras, and C. Tinelli, Abstract DPLL and Abstract DPLL Modulo Theories, Proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, pp.36-50
DOI : 10.1007/978-3-540-32275-7_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.406.7679

G. O. Passmore, Combined decision procedures for nonlinear arithmetics , real and complex, 2011.

S. A. Seshia, S. K. Lahiri, and R. E. Bryant, A hybrid SAT-based decision procedure for separation logic with uninterpreted functions, Proceedings of the 40th conference on Design automation , DAC '03, pp.425-430, 2003.
DOI : 10.1145/775832.775945

N. Smart, The Algorithmic Resolution of Diophantine Equations: A Computational Cookbook, 1998.
DOI : 10.1017/CBO9781107359994

A. Tarski, A Decision Method for Elementary Algebra and Geometry, 1948.
DOI : 10.1007/978-3-7091-9459-1_3

A. C. Ward and W. Seering, An approach to computational aids for mechanical design, Proceedings of the International Conference on Engineering Design, 1981.

V. Weispfenning, A New Approach to Quantifier Elimination for Real Algebra, Fakultät für Mathematik und Informatik: MIP. Fak. für Math. und Informatik, 1993.
DOI : 10.1007/978-3-7091-9459-1_20