A. Abate, A. Tiwari, and S. Sastry, Box invariance in biologically-inspired dynamical systems, Automatica, vol.45, issue.7, pp.1601-1610, 2009.

G. Bailey, Tilings of zonotopes: Discriminantal arrangements, oriented matroids and enumeration, 1997.

P. Baptiste, Disjunctive constraints for manufacturing scheduling: Principles and extensions, International Journal of Computer Integrated Manufacturing, vol.9, issue.4, pp.306-310, 1996.

J. Bertrane, P. Cousot, R. Cousot, J. Feret, L. Mauborgne et al., Static analysis and verification of aerospace software by abstract interpretation, AIAA Infotech@ Aerospace, The International Space System Engineering Conference: Data Systems in Aerospace-DASIA 2009, vol.1, pp.1-7, 2009.

J. Bertrane, P. Cousot, R. Cousot, J. Feret, L. Mauborgne et al., Static analysis and verification of aerospace software by abstract interpretation, Foundations and Trends® in Programming Languages, vol.2, issue.2-3, pp.71-190, 2015.
URL : https://hal.archives-ouvertes.fr/inria-00528611

B. Belin, M. Christie, and C. Truchet, Interactive urban planning with local search techniques: the sustains project, CompSust'12-3rd International Conference on Computational Sustainability, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00872981

, Interactive design of sustainable cities with a distributed local search solver, International Conference on AI and OR Techniques in Constriant Programming for Combinatorial Optimization Problems, pp.104-119, 2014.

M. Berz, Modern map methods in particle beam physics, vol.108, pp.1-318, 1999.

R. Bagnara, M. Patricia, E. Hill, and . Zaffanella, The parma polyhedra library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems, Science of Computer Programming, vol.72, issue.1-2, pp.3-21, 2008.

B. Billoud, M. Kontic, and A. Viari, Palingol: a declarative programming language to describe nucleic acids' secondary structures and to scan sequence databases, Nucleic acids research, vol.24, issue.8, pp.1395-1403, 1996.

F. Blanchini, Set invariance in control, Automatica, vol.35, issue.11, pp.1747-1767, 1999.

F. Blanchini and S. Miani, Constrained stabilization of continuous-time linear systems, Systems & control letters, vol.28, issue.2, pp.95-102, 1996.

M. Berz and K. Makino, Verified integration of odes and flows using differential algebraic methods on high-order taylor models, pp.361-369, 1998.

J. Bohne, Eine kombinatorische analyse zonotopaler raumaufteilungen. univ., diss, 1992.

R. Aaron and . Bradley, Sat-based model checking without unrolling, International Workshop on Verification, Model Checking, and Abstract Interpretation, pp.70-87, 2011.

X. Chen, E. Abraham, and S. Sankaranarayanan, Taylor model flowpipe construction for non-linear hybrid systems, IEEE 33rd Real-Time Systems Symposium, pp.183-192, 2012.

X. Chen, E. Ábrahám, and S. Sankaranarayanan, Flow*: An analyzer for non-linear hybrid systems, International Conference on Computer Aided Verification, pp.258-263, 2013.

P. Cousot and R. Cousot, Static determination of dynamic properties of programs, Proceedings of the 2nd International Symposium on Programming, 1976.

, Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints, Proceedings of POPL, pp.238-252, 1977.

, Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages, pp.21-30, 1979.

, Combination of abstractions in the astrée static analyzer, Annual Asian Computing Science Conference, pp.272-300, 2006.

P. Cousot, R. Cousot, and L. Mauborgne, The reduced product of abstract domains and the combination of decision procedures, International Conference on Foundations of Software Science and Computational Structures, pp.456-472, 2011.

H. Collavizza, F. Delobel, and M. Rueher, A note on partial consistencies over continuous domains, International Conference on Principles and Practice of Constraint Programming, pp.147-161, 1998.

H. Collavizza, F. Delobel, and M. Rueher, Comparing partial consistencies, Reliable computing, vol.5, issue.3, pp.213-228, 1999.

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, pp.84-96, 1978.

. Nv-chernikoba, Algorithm for discovering the set of all the solutions of a linear programming problem, USSR Computational Mathematics and Mathematical Physics, vol.8, issue.6, pp.282-293, 1968.

X. Chen, Reachability analysis of non-linear hybrid systems using taylor models, 2015.

G. Chabert and L. Jaulin, Contractor programming, Artificial Intelligence, vol.173, pp.1079-1100, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00428957

A. Chutinan, H. Bruce, and . Krogh, Computing polyhedral approximations to flow pipes for dynamic systems, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No. 98CH36171), vol.2, pp.2089-2094, 1998.

C. Combastel, A state bounding observer based on zonotopes, 2003.

, European Control Conference (ECC), pp.2589-2594, 2003.

B. John and . Conway, A course in functional analysis, vol.96, 2013.

P. Cousot, Semantic foundations of program analysis, Program flow analysis: theory and applications, 1981.

F. Chavanon and E. Remila, Rhombus tilings: decomposition and space structure, Discrete & Computational Geometry, vol.35, issue.2, pp.329-358, 2006.
URL : https://hal.archives-ouvertes.fr/hal-02101894

S. Michael-a-colón, . Sankaranarayanan, B. Henny, and . Sipma, Linear invariant generation using non-linear constraint solving, Proceedings of CAV, pp.420-432, 2003.

C. Combastel, Q. Zhang, and A. Lalami, Fault diagnosis based on the enclosure of parameters estimated with an adaptive observer, IFAC Proceedings Volumes, vol.41, pp.7314-7319, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00854789

N. Govert-de-bruijn, Algebraic theory of penrose's nonperiodic tilings of the plane, Kon. Nederl. Akad. Wetensch. Proc. Ser. A, vol.43, issue.84, pp.1-7, 1981.

. Ng-de-bruijn, Dualization of multigrids, Le Journal de Physique Colloques, vol.47, issue.C3, pp.3-9, 1986.

V. Desoutter and N. Destainville, Flip dynamics in three-dimensional random tilings, Journal of Physics A: Mathematical and General, vol.38, issue.1, p.17, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00123838

T. Dreossi, T. Dang, and C. Piazza, Parallelotope bundles for polynomial reachability, Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, pp.297-306, 2016.

D. Luiz-henrique, J. Figueiredo, and . Stolfi, Affine arithmetic: concepts and applications, Numerical Algorithms, vol.37, issue.1-4, pp.147-158, 2004.

D. Delmas, E. Goubault, S. Putot, J. Souyris, K. Tekkal et al., Towards an industrial use of fluctuat on safety-critical avionics software, International Workshop on Formal Methods for Industrial Critical Systems, pp.53-69, 2009.

D. Vijay, L. Silva, D. Haller, and . Kroening, Satisfiability solvers are static analysers, International Static Analysis Symposium, pp.317-333, 2012.

D. Vijay, L. Silva, D. Haller, and . Kroening, Abstract satisfaction, ACM SIGPLAN Notices, vol.49, issue.1, pp.139-150, 2014.

D. Vijay, L. Silva, D. Haller, M. Kroening, and . Tautschnig, Numeric bounds analysis with conflict-driven learning, International Conference on Tools and Algorithms for the Construction and Analysis of Systems, pp.48-63, 2012.

. N-destainville, F. Mosseri, and . Bailly, Configurational entropy of codimension-one tilings and directed membranes, Journal of statistical physics, vol.87, issue.3-4, pp.697-754, 1997.

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

. Steven-de-oliveira, , 2018.

S. Steven-de-oliveira, V. Bensalem, and . Prevosto, Polynomial invariants by linear algebra, International Symposium on Automated Technology for Verification and Analysis, pp.479-494, 2016.

, Synthesizing invariants by solving solvable loops, Proceedings of ATVA, pp.327-343, 2017.

W. M. Andreas and . Dress, Oriented matroids and penrose-type tilings, Lecture at thezSymposium on Combinatorics and Geometry, 1989.

D. Delmas and J. Souyris, Astrée: from research to industry, International Static Analysis Symposium, pp.437-451, 2007.

E. Fr-ed, W. Benhamou, and . Older, Journal of logic Programming, vol.32, issue.1, pp.1-24, 1997.

, Efficient implementation of property directed reachability, Proceedings of the International Conference on Formal Methods in Computer-Aided Design, pp.125-134, 2011.

S. Elnitsky, Rhombic tilings of polygons and classes of reduced words in coxeter groups, journal of combinatorial theory, Series A, vol.77, issue.2, pp.193-221, 1997.

A. Eggers, N. Ramdani, S. Nedialko, M. Nedialkov, and . Fränzle, Improving the sat modulo ode approach to hybrid systems analysis by combining different enclosure methods, Software & Systems Modeling, vol.14, issue.1, pp.121-148, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00747953

S. Felsner, Geometric graphs and arrangements: some chapters from combinatorial geometry, 2012.

J. Feret, Static analysis of digital filters, European Symposium on Programming, pp.33-48, 2004.
URL : https://hal.archives-ouvertes.fr/inria-00528447

J. Ferrez, K. Fukuda, and T. Liebling, Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm, European Journal of Operational Research, vol.166, issue.1, pp.35-50, 2005.

G. Frehse, C. Le-guernic, A. Donzé, S. Cotton, R. Ray et al., Spaceex: Scalable verification of hybrid systems, International Conference on Computer Aided Verification, pp.379-395, 2011.

W. Robert and . Floyd, Assigning meanings to programs, Mathematical aspects of computer science, vol.19, pp.19-32, 1967.

K. Ghorbal, E. Goubault, and S. Putot, The zonotope abstract domain taylor1+, International Conference on Computer Aided Verification, pp.627-633, 2009.

, A logical product approach to zonotope intersection, International Conference on Computer Aided Verification, pp.212-226, 2010.

K. Ghorbal, E. Goubault, and S. Putot, A logical product approach to zonotope intersection, Proceedings of CAV, pp.212-226, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01660910

S. Gaubert, E. Goubault, A. Taly, and S. Zennou, Static analysis by policy iteration on relational domains, European symposium on programming, pp.237-252, 2007.

K. Ghorbal, Static analysis of numerical programs: constrained affine sets abstract domain, 2011.
URL : https://hal.archives-ouvertes.fr/pastel-00643442

E. Gover and N. Krikorian, Determinants and the volumes of parallelotopes and zonotopes, Linear Algebra and its Applications, vol.433, issue.1, pp.28-40, 2010.

A. Girard and C. Le-guernic, Zonotope/hyperplane intersection for hybrid systems reachability analysis, International Workshop on Hybrid Systems: Computation and Control, pp.215-228, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00306993

P. Garg, C. Löding, P. Madhusudan, and D. Neider, Ice: A robust framework for learning invariants, Proceedings of CAV, pp.69-87, 2014.

D. Gerault, M. Minier, and C. Solnon, Constraint programming models for chosen key differential cryptanalysis, International Conference on Principles and Practice of Constraint Programming, pp.584-601, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01331222

P. Garg, D. Neider, P. Madhusudan, and D. Roth, Learning invariants using decision trees and implication counterexamples, ACM Sigplan Notices, vol.51, pp.499-512, 2016.

J. Leonidas, A. Guibas, L. Nguyen, and . Zhang, Zonotopes as bounding volumes, Proceedings of the ACM-SIAM symposium on Discrete algorithms, pp.803-812, 2003.

E. Goubault and S. Putot, Static analysis of numerical algorithms, International Static Analysis Symposium, pp.18-34, 2006.

, A zonotopic framework for functional abstractions, 2009.

, A zonotopic framework for functional abstractions, Formal Methods in System Design, vol.47, issue.3, pp.302-360, 2015.

, Forward inner-approximated reachability of non-linear continuous systems, Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control, pp.1-10, 2017.

E. Goubault, S. Putot, P. Baufreton, and J. Gassino, Static analysis of the accuracy in control systems: Principles and experiments, International Workshop on Formal Methods for Industrial Critical Systems, pp.3-20, 2007.

E. Goubault, S. Putot, and F. Védrine, Modular static analysis with zonotopes, International Static Analysis Symposium, pp.24-40, 2012.

T. Gawlitza and H. Seidl, Precise fixpoint computation through strategy iteration, European symposium on programming, pp.300-315, 2007.

, Precise relational invariants through strategy iteration, International Workshop on Computer Science Logic, pp.23-40, 2007.

H. Thomas-martin-gawlitza, A. Seidl, S. Adjé, É. Gaubert, and . Goubault, Abstract interpretation meets convex optimization, Journal of Symbolic Computation, vol.47, issue.12, pp.1416-1446, 2012.

S. Gulwani, S. Srivastava, and R. Venkatesan, Program analysis as constraint solving, ACM SIGPLAN Notices, vol.43, issue.6, pp.281-292, 2008.

S. Gulwani and A. Tiwari, Combining abstract interpreters, ACM SIGPLAN Notices, vol.41, pp.376-386, 2006.

, Constraint-based approach for analysis of hybrid systems, International Conference on Computer Aided Verification, pp.190-203, 2008.

K. Hoder and N. Bjørner, Generalized property directed reachability, International Conference on Theory and Applications of Satisfiability Testing, pp.157-171, 2012.

M. Hénon, A two-dimensional mapping with a strange attractor, The Theory of Chaotic Attractors, pp.94-102, 1976.

B. Hasselblatt and A. Katok, Handbook of dynamical systems, 2002.

D. Henrion and M. Korda, Convex computation of the region of attraction of polynomial control systems, IEEE Transactions on Automatic Control, vol.59, issue.2, pp.297-312, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00723019

M. Henz, S. Lauer, and D. Zimmermann, Compozeintention-based music composition through constraint programming, Tools with Artificial Intelligence, Proceedings Eighth IEEE International Conference on, pp.118-121, 1996.

C. Hoare, An axiomatic basis for computer programming, Communications of the ACM, vol.12, issue.10, pp.576-580, 1969.

O. Holtz and A. Ron, Zonotopal algebra, Advances in Mathematics, vol.227, issue.2, pp.847-894, 2011.

Z. Horváth, Y. Song, and T. Terlaky, A novel unified approach to invariance conditions for a linear dynamical system, Applied Mathematics and Computation, vol.298, pp.351-367, 2017.

, Invariance preserving discretization methods of dynamical systems, Vietnam Journal of Mathematics, vol.46, issue.4, pp.803-823, 2018.

S. Ilog, R. Hull, and . Box-consistency, Logic Programming: Proceedings of the 1999 International Conference on Logic Programming, p.230, 1999.

L. Jaulin, Solving set-valued constraint satisfaction problems, Computing, vol.94, issue.2-4, pp.297-311, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00686856

B. Jeannet and A. Miné, Apron: A library of numerical abstract domains for static analysis, Proceedings of CAV, pp.661-667, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00786354

J. Mioara-maria, Rigorous polynomial approximations and applications, 2011.

. Stephen-cole-kleene, . Ng-de-bruijn, A. De-groot, and . Cornelis-zaanen, Introduction to metamathematics, vol.483, 1952.

R. Kenyon, Tiling a polygon with parallelograms, Algorithmica 9, pp.382-397, 1993.

B. Kabi, E. Goubault, A. Mine, and S. Putot, Combining zonotope abstraction and constraint programming for synthesizing inductive invariants, International Workshop on Numerical Software Verification, 2020.

B. Kabi, E. Goubault, and S. Putot, A concoction of zonotope abstraction and constraint programming for finding an invariant, 2016.

F. Kirchner, N. Kosmatov, and V. Prevosto, Combining zonotope abstraction and constraint programming for finding an invariant, Formal Aspects of Computing, vol.27, issue.3, pp.573-609, 2015.

D. Egor-george-karpenkov, P. Monniaux, and . Wendler, Program analysis with local policy iteration, International Conference on Verification, Model Checking, and Abstract Interpretation, pp.127-146, 2016.

M. Latapy, Generalized integer partitions, tilings of zonotopes and lattices, Formal Power Series and Algebraic Combinatorics, pp.256-267, 2000.

S. Lyonnard, G. Coddens, Y. Calvayrac, and D. Gratias, Atomic (phason) hopping in perfect icosahedral quasicrystals al 70.3 pd 21.4 mn 8.3 by time-of-flight quasielastic neutron scattering, Physical Review B, vol.53, issue.6, p.3150, 1996.

L. Thomas-le-mézo, B. Jaulin, and . Zerr, An interval approach to compute invariant sets, IEEE Transactions on Automatic Control, vol.62, issue.8, pp.4236-4242, 2017.

P. Lacan, J. N. Monfort, . Ribal, G. Deutsch, and . Gonthier, Ariane 5-the software reliability verification process, DASIA 98-Data Systems in Aerospace, vol.422, p.201, 1998.

C. L. Pape, Using a constraint-based scheduling library to solve a specific scheduling problem, 1994.

C. Vu-tuan-hieu-le, T. Stoica, E. F. Alamo, D. Camacho, and . Dumur, Zonotope-based set-membership estimation for multi-output uncertain systems, IEEE International Symposium on Intelligent Control (ISIC), pp.212-217, 2013.

V. Hervé-le, A note on chernikova's algorithm, 1992.

J. Liu, N. Zhan, and H. Zhao, Computing semialgebraic invariants for polynomial dynamical systems, Proceedings of the ninth ACM international conference on Embedded software, pp.97-106, 2011.

A. Miné, Tutorial on static inference of numeric invariants by abstract interpretation, Foundations and Trends® in Programming Languages, vol.4, issue.3-4, pp.120-372, 2017.

A. K. Mackworth, Consistency in networks of relations, vol.8, pp.99-118, 1977.

, On reading sketch maps, 1977.

B. Martin, Rigorous algorithms for nonlinear biobjective optimization, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01146856

L. Mauborgne, Astrée: Verification of absence of runtime error, Building the Information Society, pp.385-392, 2004.

K. Makino and M. Berz, Taylor models and other validated functional inclusion methods, International Journal of Pure and Applied Mathematics, vol.6, pp.239-316, 2003.

, Rigorous integration of flows and odes using taylor models, Proceedings of the 2009 conference on Symbolic Numeric Computation, pp.79-84, 2009.

A. Miné, J. Breck, and T. Reps, An algorithm inspired by constraint solvers to infer inductive invariants in numeric programs, Proceedings of ESOP, pp.560-588, 2016.

P. Mcmullen, On zonotopes, Transactions of the American Mathematical Society, vol.159, pp.91-109, 1971.

. Peter-mcmullen, Polytopes with centrally symmetric facets, Israel Journal of Mathematics, vol.23, issue.3-4, pp.337-338, 1976.

A. Miné, A new numerical abstract domain based on differencebound matrices, Programs as Data Objects, pp.155-172, 2001.

, Weakly relational numerical abstract domains.(domaines numériques abstraits faiblement relationnels, 2004.

, The octagon abstract domain, Higher-order and symbolic computation, vol.19, pp.31-100, 2006.

K. Mischaikow, The conley index theory: a brief introduction, Banach Center Publications, vol.47, issue.1, pp.9-19, 1999.

U. Montanari, Networks of constraints: Fundamental properties and applications to picture processing, Information sciences, vol.7, pp.95-132, 1974.

E. Ramon and . Moore, , 1966.

S. Nedialko, . Nedialkov, G. Kenneth-r-jackson, and . Corliss, Validated solutions of initial value problems for ordinary differential equations, Applied Mathematics and Computation, vol.105, issue.1, pp.21-68, 1999.

G. Nelson and D. C. Oppen, Simplification by cooperating decision procedures, ACM Transactions on Programming Languages and Systems (TOPLAS), vol.1, issue.2, pp.245-257, 1979.

S. Negaard-paper, Attractors and attracting neighborhoods for multiflows, 2019.

. Duong-nguyen-que, Robust and generic abstract domain for static program analyses: the polyhedral case, 2010.

A. Platzer and E. M. Clarke, Computing differential invariants of hybrid systems as fixedpoints, Formal Methods in System Design, vol.35, issue.1, pp.98-120, 2009.

M. Pelleau, Abstract domains in constraint programming, Elsevier, 2015.

O. Ponsini, C. Michel, and M. Rueher, Combining constraint programming and abstract interpretation for value analysis of floating-point programs, IEEE Fifth International Conference on Software Testing, Verification and Validation, pp.775-776, 2012.

M. Pelleau, A. Miné, C. Truchet, and F. Benhamou, A constraint solver based on abstract domains, International Workshop on Verification, Model Checking, and Abstract Interpretation, pp.434-454, 2013.

M. Pelleau, C. Truchet, and F. Benhamou, Octagonal domains for continuous constraints, International Conference on Principles and Practice of Constraint Programming, pp.706-720, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00785598

, The octagon abstract domain for continuous constraints, Constraints, vol.19, issue.3, pp.309-337, 2014.

V. Reiner, The generalized baues problem, New perspectives in algebraic combinatorics, vol.38, pp.293-336, 1999.

P. Roux and P. Garoche, Integrating policy iterations in abstract interpreters, Automated Technology for Verification and Analysis, pp.240-254, 2013.

, Computing quadratic invariants with min-and max-policy iterations: A practical comparison, International Symposium on Formal Methods, pp.563-578, 2014.

, Practical policy iterations, vol.46, pp.163-196, 2015.

J. Richter, -. Günter, and M. Ziegler, Zonotopal tilings and the bohne-dress theorem, vol.178, pp.211-211, 1994.

R. Henry-gordon, Classes of recursively enumerable sets and their decision problems, Transactions of the American Mathematical Society, vol.74, issue.2, pp.358-366, 1953.

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

S. Xin-chen-rwth, E. Sankaranarayanan, and . Ábrahám, Under-approximate flowpipes for non-linear continuous systems, 2014.

, Formal Methods in Computer-Aided Design (FMCAD), pp.59-66, 2014.

T. Reps, M. Sagiv, and G. Yorsh, Symbolic implementation of the best transformer, International Workshop on Verification, Model Checking, and Abstract Interpretation, pp.252-266, 2004.

T. Reps and A. Thakur, Automating abstract interpretation, International Conference on Verification, Model Checking, and Abstract Interpretation, pp.3-40, 2016.

G. Rubino, Experimental evaluation of numerical domains for inferring ranges, Electronic Notes in Theoretical Computer Science, vol.334, pp.3-16, 2018.

M. Rueher, Solving continuous constraint systems, International Conference on Computer Graphics and Artificial Intelligence, vol.1, pp.2-2, 2005.

D. Ruelle, What is a strange attractor, Notices of the AMS, vol.53, issue.7, pp.764-765, 2006.

P. Richard and . Stanley, An introduction to hyperplane arrangements, Geometric combinatorics, vol.13, pp.389-496, 2004.

D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Metallic phase with long-range orientational order and no translational symmetry, Physical review letters, vol.53, issue.20, 1951.

D. Julien-alexandre, A. Sandretto, and . Chapoutot, Validated simulation of differential algebraic equations with runge-kutta methods

A. Schrijver, Theory of linear and integer programming, 1998.

J. Souyris and D. Delmas, Experimental assessment of astrée on safety-critical avionics software, International Conference on Computer Safety, Reliability, and Security, pp.479-490, 2007.

J. Stolfi, L. Si, H. Dai, M. Raghothaman, M. Naik et al., Learning loop invariants for program verification, Self-validated numerical methods and applications, Monograph for 21st Brazilian Mathematics Colloquium, IMPA, pp.7762-7773, 1997.

P. Shaw, Using constraint programming and local search methods to solve vehicle routing problems, International conference on principles and practice of constraint programming, pp.417-431, 1998.

C. Geoffrey and . Shephard, Combinatorial properties of associated zonotopes, Canadian Journal of Mathematics, vol.26, issue.2, pp.302-321, 1974.

D. Sam, -. , and B. Faltings, Consistency techniques for continuous constraints, vol.1, pp.85-118, 1996.

A. Sogokon, B. Paul, and T. Jackson, Verifying safety and persistence properties of hybrid systems using flowpipes and continuous invariants, NASA Formal Methods Symposium, pp.194-211, 2017.

S. Schupp, J. Nellen, and E. Ábrahám, Divide and conquer: Variable set separation in hybrid systems reachability analysis, 2017.

J. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes, 1985.

G. Singh, M. Püschel, and M. Vechev, Fast polyhedra abstract domain, ACM SIGPLAN Notices, vol.52, pp.46-59, 2017.

S. Sankaranarayanan, B. Henny, Z. Sipma, and . Manna, Constructing invariants for hybrid systems, International Workshop on Hybrid Systems: Computation and Control, pp.539-554, 2004.

, Scalable analysis of linear systems using mathematical programming, International Workshop on Verification, Model Checking, and Abstract Interpretation, pp.25-41, 2005.

P. Richard and . Stanley, Hyperplane arrangements, parking functions and tree inversions, Mathematical essays in honor of Gian-Carlo Rota, pp.359-375, 1998.

S. Sternberg, Dynamical systems, Courier Corporation, 2010.

L. Shen, M. Wu, Z. Yang, and Z. Zeng, Finding positively invariant sets of a class of nonlinear loops via curve fitting, pp.185-190, 2009.

C. Truchet, G. Assayag, and P. Codognet, Visual and adaptive constraint programming in music, ICMC, 2001.
URL : https://hal.archives-ouvertes.fr/hal-01105723

A. Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific journal of Mathematics, vol.5, issue.2, pp.285-309, 1955.

A. Thakur, M. Elder, and T. Reps, Bilateral algorithms for symbolic abstraction, International Static Analysis Symposium, pp.111-128, 2012.

A. Thakur, A. Lal, J. Lim, and T. Reps, Posthat and all that: Automating abstract interpretation, Electronic Notes in Theoretical Computer Science, vol.311, pp.15-32, 2015.

[. Bibliography, J. Ts13]-s-mojtaba-tabatabaeipour, and . Stoustrup, Set-membership state estimation for discrete time piecewise affine systems using zonotopes, European Control Conference (ECC), pp.3143-3148, 2013.

M. Alan and . Turing, On computable numbers, with an application to the entscheidungsproblem, Proceedings of the London mathematical society, vol.2, issue.1, pp.230-265, 1937.

C. Urban, Static analysis by abstract interpretation of functional temporal properties of programs, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01176641

Y. Vizel, A. Gurfinkel, S. Shoham, and S. Malik, Ic3-flipping the e in ice, International Conference on Verification, Model Checking, and Abstract Interpretation, pp.521-538, 2017.

H. Wen, A review of the hénon map and its physical interpretations, Sch. Phys. Georg. Inst. Technol. Atlanta, pp.1-9, 2014.

H. Weyl, Elementare theorie der konvexen polyeder, Commentarii Mathematici Helvetici, vol.7, issue.1, pp.290-306, 1934.

J. Wan, J. Vehi, and N. Luo, A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality, Journal of Global Optimization, vol.44, issue.3, pp.395-407, 2009.

M. Günter and . Ziegler, Lectures on polytopes, vol.152, 2012.

M. Günter, J. Ziegler, and . Richter-gebert, Oriented matroids, Handbook of Discrete and Computational Geometry, vol.6, pp.159-184, 2017.

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