P. Cousot and N. Halbwachs, Automatic discovery of linear restraints among variables of a program, Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '78, pp.84-97, 1978.
DOI : 10.1145/512760.512770

N. Halbwachs, Détermination automatique de relations linéaires vérifiées par les variables d'un programme, Thèse du 3` eme cycle, 1979.

P. Cousot and R. Cousot, Abstract interpretation, Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '77, pp.238-252, 1977.
DOI : 10.1145/512950.512973
URL : https://hal.archives-ouvertes.fr/inria-00528590

F. Irigoin, P. Jouvelot, and R. Triolet, Semantical interprocedural parallelization: An overview of the PIPS project, ACM Int. Conf. on Supercomputing, ICS'91, pp.244-251, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00984684

N. Halbwachs, Y. Proy, and P. Roumanoff, Verification of real-time systems using linear relation analysis, Formal Methods in System Design, vol.11, issue.2, pp.157-185, 1997.
DOI : 10.1023/A:1008678014487

T. A. Henzinger, P. Ho, and H. Wong-toi, HYTECH: a??model checker for hybrid systems, International Journal on Software Tools for Technology Transfer, vol.1, issue.1-2, pp.110-122, 1997.
DOI : 10.1007/s100090050008

N. Dor, M. Rodeh, and M. Sagiv, Cleanness Checking of String Manipulations in C Programs via Integer Analysis, Static Analysis Symposium, pp.194-212, 2001.
DOI : 10.1007/3-540-47764-0_12

N. Bjorner, I. A. Browne, and Z. Manna, Automatic generation of invariants and intermediate assertions, Theoretical Computer Science, vol.173, issue.1, pp.49-87, 1997.
DOI : 10.1016/S0304-3975(96)00191-0

P. Roux, R. Delmas, and P. Garoche, SMT-AI: an Abstract Interpreter as Oracle for k-induction, Electronic Notes in Theoretical Computer Science, vol.267, issue.2, pp.55-68, 2010.
DOI : 10.1016/j.entcs.2010.09.018

N. Halbwachs, Delay analysis in synchronous programs, Computer-Aided Verification, pp.333-346, 1993.
DOI : 10.1007/3-540-56922-7_28

A. Simon and A. King, Widening Polyhedra with Landmarks, Asian Symposium on Programming Languages and Systems LNCS, vol.4279, pp.166-182, 2006.
DOI : 10.1007/11924661_11

D. Gopan and T. W. Reps, Guided Static Analysis, Static Analysis Symposium, pp.349-365, 2007.
DOI : 10.1007/978-3-540-74061-2_22

B. Boigelot and P. Wolper, Symbolic verification with periodic sets, Computer-Aided Verification, pp.55-67, 1994.
DOI : 10.1007/3-540-58179-0_43

P. Wolper and B. Boigelot, Verifying systems with infinite but regular state spaces, Computer-Aided Verification, pp.88-97, 1998.
DOI : 10.1007/BFb0028736

H. Comon and Y. Jurski, Multiple counters automata, safety analysis and presburger arithmetic, Computer-Aided Verification, pp.268-279, 1998.
DOI : 10.1007/BFb0028751

A. Finkel and G. Sutre, An Algorithm Constructing the Semilinear Post for 2-Dim Reset/Transfer VASS, Mathematical Foundations of computer science LNCS, vol.1893, pp.353-362, 2000.
DOI : 10.1007/3-540-44612-5_31

S. Bardin, A. Finkel, J. Leroux, and L. Petrucci, FAST: Fast Acceleration of Symbolic Transition Systems, Computer-Aided Verification, pp.118-121, 2003.
DOI : 10.1007/978-3-540-45069-6_12
URL : https://hal.archives-ouvertes.fr/hal-00084185

L. Gonnord and N. Halbwachs, Combining Widening and Acceleration in Linear Relation Analysis, Static Analysis Symposium, pp.144-160, 2006.
DOI : 10.1007/11823230_10
URL : https://hal.archives-ouvertes.fr/hal-00189614

T. Motzkin, H. Raiffa, G. Thompson, and R. , 3. The Double Description Method, Contributions to the theory of games, 1953.
DOI : 10.1515/9781400881970-004

K. Fukuda and A. Prodon, Double description method revisited, Combinatorics and Computer Science LNCS, vol.1120, pp.91-111, 1995.
DOI : 10.1007/3-540-61576-8_77

N. V. Chernikova, Algorithm for finding a general formula for the non-negative solutions of a system of linear inequalities, USSR Computational Mathematics and Mathematical Physics, vol.5, issue.2, pp.228-233, 1965.
DOI : 10.1016/0041-5553(65)90045-5

H. L. Verge, A note on Chernikowa's algorithm, IRISA, 1992.

H. P. Williams, Fourier's Method of Linear Programming and Its Dual, The American Mathematical Monthly, vol.93, issue.9, pp.681-695, 1986.
DOI : 10.2307/2322281

P. Cousot and R. Cousot, Comparing the Galois connection and widening/narrowing approaches to abstract interpretation, Programming Language Implementation and Logic Programming, pp.269-295, 1992.
DOI : 10.1007/3-540-55844-6_142

F. Bourdoncle, Efficient chaotic iteration strategies with widenings, LNCS, vol.735, pp.128-141, 1993.
DOI : 10.1007/BFb0039704

L. Gonnord, Accélération abstraite pour l'amélioration de la précision en analyse des relations linéaires, Thèse de doctorat, 2007.

L. Gonnord and N. Halbwachs, Abstract acceleration in linear relation analysis, Science of Computer Programming, vol.93, 2010.
DOI : 10.1016/j.scico.2013.09.016
URL : https://hal.archives-ouvertes.fr/hal-00785116

L. Lakhdar-chaouch, B. Jeannet, and A. Girault, Widening with Thresholds for Programs with Complex Control Graphs, LNCS, vol.6996, pp.492-502, 2011.
DOI : 10.1007/978-3-540-77505-8_23
URL : https://hal.archives-ouvertes.fr/inria-00635243

B. Boigelot and P. Godefroid, Symbolic verification of communication protocols with infinite state spaces using QDDs, Formal Methods in System Design, vol.14, issue.3, pp.237-255, 1997.
DOI : 10.1007/3-540-61474-5_53

L. Fribourg and H. Olsén, Proving safety properties of infinite state systems by compilation into Presburger arithmetic, Concurrency Theory, pp.213-227, 1997.
DOI : 10.1007/3-540-63141-0_15

B. Boigelot, Symbolic methods for exploring infinite state spaces, 1998.

S. Bardin, A. Finkel, J. Leroux, and P. Schnoebelen, Flat Acceleration in Symbolic Model Checking, LNCS, vol.3707, pp.474-488, 2005.
DOI : 10.1007/11562948_35
URL : https://hal.archives-ouvertes.fr/hal-00346302

M. L. Minsky, Computation: Finite and Infinite Machines, 1967.

W. Kelly, W. Pugh, E. Rosser, and T. Shpeisman, Transitive Closure of Infinite Graphs and Its Applications, International Journal of Parallel Programming, vol.36, issue.12, pp.579-598, 1996.
DOI : 10.1145/209936.209952

A. Finkel and J. Leroux, How to compose Presburger-accelerations: Applications to broadcast protocols, in: Foundations of Software Technology and Theoretical Computer Science, LNCS, vol.2556, pp.145-156, 2002.

J. Leroux and G. Sutre, Flat Counter Automata Almost Everywhere!, LNCS, vol.3707, pp.489-503, 2005.
DOI : 10.1007/11562948_36
URL : https://hal.archives-ouvertes.fr/hal-00346310

J. Leroux, Algorithmique de la vérification des systèmessystèmes`systèmesà compteurs ? approximation et accélération ? implémentation dans l'outil FAST, Thèse de doctorat, 2003.

S. Bardin, A. Finkel, and J. Leroux, FASTer Acceleration of Counter Automata in Practice, LNCS, vol.2988, pp.576-590, 2004.
DOI : 10.1007/978-3-540-24730-2_42

S. Bardin, A. Finkel, J. Leroux, and L. Petrucci, FAST: acceleration from theory to practice, International Journal on Software Tools for Technology Transfer, vol.15, issue.2, pp.401-424, 2008.
DOI : 10.1016/S0022-0000(69)80011-5
URL : https://hal.archives-ouvertes.fr/hal-00345968

P. Lancaster and M. Tismenetsky, The Theory of Matrices, 1984.

P. Schrammel, Logico-numerical verification methods for discrete and hybrid systems, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00809357

E. Asarin, O. Maler, and A. Pnueli, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, pp.35-65, 1995.
DOI : 10.1016/0304-3975(94)00228-B

J. Henry, D. Monniaux, and M. Moy, Succinct Representations for Abstract Interpretation, Static Analysis Symposium, pp.283-299, 2012.
DOI : 10.1007/978-3-642-33125-1_20
URL : https://hal.archives-ouvertes.fr/hal-00709833

D. Monniaux and L. Gonnord, Using Bounded Model Checking to Focus Fixpoint Iterations, Static Analysis Symposium, pp.369-385, 2011.
DOI : 10.1007/11823230_2
URL : https://hal.archives-ouvertes.fr/hal-00600087

P. Schrammel and B. Jeannet, Extending Abstract Acceleration Methods to Data-Flow Programs with Numerical Inputs, Numerical and Symbolic Abstract Domains, pp.101-114, 2010.
DOI : 10.1016/j.entcs.2010.09.009
URL : https://hal.archives-ouvertes.fr/hal-00749914

P. Schrammel and B. Jeannet, Applying abstract acceleration to (co-)reachability analysis of reactive programs, Journal of Symbolic Computation, vol.47, issue.12, pp.1512-1532, 2012.
DOI : 10.1016/j.jsc.2011.12.051
URL : https://hal.archives-ouvertes.fr/hal-00753412

N. Halbwachs, P. Caspi, P. Raymond, and D. Pilaud, The synchronous data flow programming language LUSTRE, Proceedings of the IEEE, vol.79, issue.9, pp.1305-1320, 1991.
DOI : 10.1109/5.97300

B. Jeannet, Dynamic partitioning in linear relation analysis. application to the verification of reactive systems, Formal Methods in System Design, vol.23, issue.1, pp.5-37, 2003.
DOI : 10.1023/A:1024480913162

P. Schrammel and B. Jeannet, Logico-Numerical Abstract Acceleration and Application to the Verification of Data-Flow Programs, Static Analysis Symposium, pp.233-248, 2011.
DOI : 10.1007/s10703-006-0031-0
URL : https://hal.archives-ouvertes.fr/hal-00750762

P. Feautrier and L. Gonnord, Accelerated Invariant Generation for C Programs with Aspic and C2fsm, Electronic Notes in Theoretical Computer Science, vol.267, issue.2, pp.3-13, 2010.
DOI : 10.1016/j.entcs.2010.09.014
URL : https://hal.archives-ouvertes.fr/inria-00523320

C. Alias, A. Darte, P. Feautrier, and L. Gonnord, Multi-dimensional Rankings, Program Termination, and Complexity Bounds of Flowchart Programs, Static Analysis Symposium, pp.117-133, 2010.
DOI : 10.1007/978-3-642-15769-1_8
URL : https://hal.archives-ouvertes.fr/inria-00523298

P. Caspi, D. Pilaud, N. Halbwachs, and J. A. Plaice, LUSTRE: a declarative language for real-time programming, Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '87, pp.178-188, 1987.
DOI : 10.1145/41625.41641

B. Jeannet and A. Miné, Apron: A Library of Numerical Abstract Domains for Static Analysis, Computer-Aided Verification, pp.661-667, 2009.
DOI : 10.1007/3-540-45013-0_7
URL : https://hal.archives-ouvertes.fr/hal-00786354

B. Jeannet, Some Experience on the Software Engineering of Abstract Interpretation Tools, Electronic Notes in Theoretical Computer Science, vol.267, issue.2, 2010.
DOI : 10.1016/j.entcs.2010.09.016
URL : https://hal.archives-ouvertes.fr/hal-00786328

B. Jeannet, Partitionnement dynamique dans l'analyse de relations linéaires et applicationàapplication`applicationà la vérification de programmes synchrones, Thèse de doctorat, 2000.

P. Caspi, G. Hamon, and M. Pouzet, Synchronous Functional Programming with Lucid Synchrone, Real-Time Systems: Description and Verification Techniques: Theory and Tools, 2008.
DOI : 10.1002/9780470611012.ch7

K. Ku, T. Hart, M. Chechik, and D. Lie, A buffer overflow benchmark for software model checkers, Proceedings of the twenty-second IEEE/ACM international conference on Automated software engineering , ASE '07, pp.389-392, 2007.
DOI : 10.1145/1321631.1321691

A. Gupta and A. Rybalchenko, InvGen: An Efficient Invariant Generator, pp.634-640, 2009.
DOI : 10.1007/3-540-45937-5_16

N. Halbwachs and J. Henry, When the Decreasing Sequence Fails, Static Analysis Symposium, pp.198-213, 2012.
DOI : 10.1007/978-3-642-33125-1_15
URL : https://hal.archives-ouvertes.fr/hal-00734340

P. Cousot, R. Cousot, J. Feret, L. Mauborgne, A. Miné et al., Why does Astr??e scale up?, Formal Methods in System Design, vol.345, issue.1, pp.229-264, 2009.
DOI : 10.1007/s10703-009-0089-6

C. Wang, Z. Yang, A. Gupta, and F. Ivancic, Using Counterexamples for Improving the Precision of Reachability Computation with Polyhedra, Computer-Aided Verification, pp.352-365, 2007.
DOI : 10.1007/978-3-540-73368-3_40

R. Bagnara, P. M. Hill, E. Ricci, and E. Zaffanella, Precise widening operators for convex polyhedra, Static Analysis Symposium, pp.337-354, 2003.

R. Bagnara, P. M. Hill, and E. Zaffanella, Widening operators for powerset domains, Model Checking, and Abstract Interpretation, pp.135-148, 2004.

J. B. Kam and J. D. Ullman, Monotone data flow analysis frameworks, Acta Informatica, vol.2, issue.3, pp.305-317, 1977.
DOI : 10.1007/BF00290339

J. Leroux and G. Sutre, Acceleration in Convex Data-Flow Analysis, Foundations of Software Technology and Theoretical Computer Science LNCS, vol.4855, pp.520-531, 2007.
DOI : 10.1007/978-3-540-77050-3_43
URL : https://hal.archives-ouvertes.fr/hal-00346295

C. Ancourt, F. Coelho, and F. Irigoin, A Modular Static Analysis Approach to Affine Loop Invariants Detection, Numerical and Symbolic Abstract Domains, pp.3-16, 2010.
DOI : 10.1016/j.entcs.2010.09.002
URL : https://hal.archives-ouvertes.fr/hal-00586338

A. Beletska, D. Barthou, W. Bielecki, and A. Cohen, Computing the Transitive Closure of a Union of Affine Integer Tuple Relations, Combinatorial Optimization and Applications, pp.98-109, 2009.
DOI : 10.1007/BF03356760
URL : https://hal.archives-ouvertes.fr/hal-00575959

S. Verdoolaege, A. Cohen, and A. Beletska, Transitive Closures of Affine Integer Tuple Relations and Their Overapproximations, Static Analysis Symposium, pp.216-232, 2011.
DOI : 10.1007/978-3-642-02658-4_44
URL : https://hal.archives-ouvertes.fr/hal-00645221

S. Sankaranarayanan, H. B. Sipma, and Z. Manna, Scalable Analysis of Linear Systems Using Mathematical Programming, Model Checking, and Abstract Interpretation, pp.25-41, 2005.
DOI : 10.1007/978-3-540-30579-8_2

Z. Su and D. Wagner, A Class of Polynomially Solvable Range Constraints for Interval Analysis without Widenings and Narrowings, LNCS, vol.2988, pp.280-295, 2004.
DOI : 10.1007/978-3-540-24730-2_23

A. Costan, S. Gaubert, E. Goubault, M. Martel, and S. Putot, A Policy Iteration Algorithm for Computing Fixed Points in Static Analysis of Programs, Computer-Aided Verification, pp.462-475, 2005.
DOI : 10.1007/11513988_46

T. Gawlitza and H. Seidl, Precise Fixpoint Computation Through Strategy Iteration, ESOP 2007, pp.300-315, 2007.
DOI : 10.1007/978-3-540-71316-6_21

T. M. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, and ´. E. Goubault, Abstract interpretation meets convex optimization, Journal of Symbolic Computation, vol.47, issue.12, pp.1512-1532, 2012.
DOI : 10.1016/j.jsc.2011.12.048
URL : https://hal.archives-ouvertes.fr/hal-00778070

M. Bozga, C. G??rleag??rlea, and R. Iosif, Iterating Octagons, LNCS, vol.19, issue.1, pp.337-351, 2009.
DOI : 10.1007/s10990-006-8609-1
URL : https://hal.archives-ouvertes.fr/hal-01418910

M. Bozga, R. Iosif, and F. Konecn´ykonecn´y, Fast Acceleration of Ultimately Periodic Relations, Computer-Aided Verification, pp.227-242, 2010.
DOI : 10.1007/978-3-642-14295-6_23
URL : https://hal.archives-ouvertes.fr/hal-01418908

H. Hojjat, R. Iosif, F. Kone?n´kone?n´y, V. Kuncak, and P. Rümmer, Accelerating Interpolants, LNCS, vol.7561, 2012.
DOI : 10.1007/978-3-642-33386-6_16
URL : https://hal.archives-ouvertes.fr/hal-01418900

A. Kurzhanskiy and P. Varaiya, Ellipsoidal Techniques for Reachability Analysis, Hybrid Systems: Computation and Control, pp.202-214, 2000.
DOI : 10.1007/3-540-46430-1_19

J. Feret, Static Analysis of Digital Filters, European Symposium on Programming, pp.33-48, 2004.
DOI : 10.1007/978-3-540-24725-8_4
URL : https://hal.archives-ouvertes.fr/inria-00528447

P. Roux, R. Jobredeaux, P. Garoche, and E. Feron, A generic ellipsoid abstract domain for linear time invariant systems, Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control, HSCC '12, pp.105-114, 2012.
DOI : 10.1145/2185632.2185651
URL : https://hal.archives-ouvertes.fr/hal-00608673

L. Kovács, Invariant Generation for P-Solvable Loops with Assignments, Computer Science -Theory and Applications LNCS, vol.5010, pp.349-359, 2008.
DOI : 10.1007/978-3-540-79709-8_35

A. Tiwari, Approximate Reachability for Linear Systems, LNCS, vol.2623, pp.514-525, 2003.
DOI : 10.1007/3-540-36580-X_37

S. Sankaranarayanan and A. Tiwari, Relational Abstractions for Continuous and Hybrid Systems, Computer-Aided Verification, pp.686-702, 2011.
DOI : 10.1007/s10703-007-0044-3

S. Sankaranarayanan, H. B. Sipma, and Z. Manna, Constraint-Based Linear-Relations Analysis, LNCS, vol.3148, pp.53-68, 2004.
DOI : 10.1007/978-3-540-27864-1_7

M. Colón, S. Sankaranarayanan, and H. Sipma, Linear Invariant Generation Using Non-linear Constraint Solving, Computer-Aided Verification, pp.420-432, 2003.
DOI : 10.1007/978-3-540-45069-6_39

S. Srivastava and S. Gulwani, Program verification using templates over predicate abstraction, in: Programming language design and implementation, pp.223-234, 2009.

S. Gulwani and A. Tiwari, Constraint-Based Approach for Analysis of Hybrid Systems, Computer-Aided Verification, pp.190-203, 2008.
DOI : 10.1007/978-3-540-70545-1_18

H. Hojjat, F. Konecny, F. Garnier, R. Iosif, V. Kuncak et al., A verification toolkit for numerical transition systems (tool paper), in: Formal Methods, LNCS, vol.7436, 2012.