R. Allen and K. Kennedy, Optimizing compilers for modern architectures: a dependence-based approach, p.35, 2002.

P. Alves, F. Gruber, J. Doerfert, A. Lamprineas, T. Grosser et al., Runtime pointer disambiguation, Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications, OOPSLA 2015, pp.589-606, 2015.
DOI : 10.1145/2814270.2814285
URL : https://hal.archives-ouvertes.fr/hal-01234086

. Apple, clang: a c language family frontend for llvm, p.25, 2007.

C. Bastoul, Code generation in the polyhedral model is easier than you think, Proceedings. 13th International Conference on Parallel Architecture and Compilation Techniques, 2004. PACT 2004., pp.7-16, 2004.
DOI : 10.1109/PACT.2004.1342537
URL : https://hal.archives-ouvertes.fr/hal-00017260

M. Benabderrahmane, C. Bastoul, L. Pouchet, and A. Cohen, A Conservative Approach to Handle Full Functions in the Polyhedral Model, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00356818

A. J. Bik, Software Vectorization Handbook, The: Applying Intel Multimedia Extensions for Maximum Performance, p.53, 2004.

U. Bondhugula, A. Hartono, J. Ramanujam, and P. Sadayappan, Pluto: A practical and fully automatic polyhedral program optimization system, Proceedings of the ACM SIGPLAN 2008 Conference on Programming Language Design and Implementation (PLDI 08), p.72, 2008.

U. K. Bondhugula, Effective Automatic Parallelization and Locality Optimization Using the Polyhedral Model, p.17, 2008.

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

P. Charles, C. Grothoff, V. Saraswat, C. Donawa, A. Kielstra et al., X10: An object-oriented approach to non-uniform cluster computing, Proceedings of the 20th Annual ACM SIGPLAN Conference on Object-oriented Programming, Systems, Languages, and Applications, OOPSLA '05, pp.519-538, 2005.

P. Clauss, F. Fernandez, D. Garbervetsky, and S. Verdoolaege, Symbolic polynomial maximization over convex sets and its application to memory requirement estimation. Very Large Scale Integration (VLSI) Systems, IEEE Transactions on, vol.17, issue.8, pp.983-996, 2009.
DOI : 10.1109/tvlsi.2008.2002049
URL : https://hal.archives-ouvertes.fr/inria-00504617

P. Clauss and I. Tchoupaeva, A Symbolic Approach to Bernstein Expansion for Program Analysis and Optimization, pp.120-133, 2004.
DOI : 10.1007/978-3-540-24723-4_9
URL : http://icps.u-strasbg.fr/upload/icps-2004-114.pdf

C. Cohen and A. Mahboubi, A Formal Quantifier Elimination for Algebraically Closed Fields, pp.189-203, 2010.
DOI : 10.1007/978-3-642-14128-7_17
URL : https://hal.archives-ouvertes.fr/inria-00464237

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.84-96, 1978.
DOI : 10.1145/512760.512770

J. H. Davenport and J. Heintz, Real quantifier elimination is doubly exponential, Journal of Symbolic Computation, vol.5, issue.1-2, pp.29-35, 1988.
DOI : 10.1016/S0747-7171(88)80004-X
URL : https://doi.org/10.1016/s0747-7171(88)80004-x

A. Dolzmann and T. Sturm, REDLOG, ACM SIGSAM Bulletin, vol.31, issue.2, pp.2-9, 1997.
DOI : 10.1145/261320.261324

V. Elango, F. Rastello, L. Pouchet, J. Ramanujam, and P. Sadayappan, On characterizing the data access complexity of programs, Proceedings of the 42Nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '15, pp.567-580, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01104556

V. Elango, N. Sedaghati, F. Rastello, L. Pouchet, J. Ramanujam et al., On Using the Roofline Model with Lower Bounds on Data Movement, ACM Transactions on Architecture and Code Optimization, vol.11, issue.4, pp.1-67, 2015.
DOI : 10.1145/1498765.1498785
URL : https://hal.archives-ouvertes.fr/hal-01104765

N. Fauzia, V. Elango, M. Ravishankar, J. Ramanujam, F. Rastello et al., Beyond reuse distance analysis, ACM Transactions on Architecture and Code Optimization, vol.10, issue.4, pp.53-71, 2013.
DOI : 10.1145/2541228.2555309
URL : https://hal.archives-ouvertes.fr/hal-00920031

P. Feautrier, Array expansion, 2nd International Conference on Supercomputing (ICS'88), pp.429-441, 1988.
DOI : 10.1145/55364.55406
URL : https://hal.archives-ouvertes.fr/hal-01099746

P. Feautrier, Parametric integer programming, RAIRO - Operations Research, vol.22, issue.3, pp.243-268, 1988.
DOI : 10.1051/ro/1988220302431

P. Feautrier, Some efficient solutions to the affine scheduling problem. I. One-dimensional time, International Journal of Parallel Programming, vol.40, issue.6, pp.313-347, 1992.
DOI : 10.1145/360827.360844

P. Feautrier, Some efficient solutions to the affine scheduling problem. Part II. Multidimensional time, International Journal of Parallel Programming, vol.2, issue.4, pp.389-420, 1992.
DOI : 10.1007/BF01379404

P. Feautrier, The power of polynomials, 5th International Workshop on Polyhedral Compilation Techniques, p.52, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01094787

A. Grö¨slingergrö¨slinger, The Challenges of Non-linear Parameters and Variables in Automatic Loop Parallelisation, pp.17-51, 2009.

T. Grosser, A. Groesllinger, and C. Lengauer, Polly -performing polyhedral optimizations on a low-level intermediate representation. Parallel Processing Letters, pp.4-17, 2012.

T. Grosser, S. Pop, J. Ramanujam, and P. Sadayappan, On recovering multi-dimensional arrays in polly, 5th International Workshop on Polyhedral Compilation Techniques, p.52, 2015.

T. Grosser, J. Ramanujam, L. Pouchet, P. Sadayappan, and S. Pop, Optimistic Delinearization of Parametrically Sized Arrays, Proceedings of the 29th ACM on International Conference on Supercomputing, ICS '15, pp.351-360, 2015.
DOI : 10.1007/11587514_15

T. Henretty, R. Veras, F. Franchetti, L. Pouchet, J. Ramanujam et al., A stencil compiler for short-vector SIMD architectures, Proceedings of the 27th international ACM conference on International conference on supercomputing, ICS '13, pp.13-24, 2013.
DOI : 10.1145/2464996.2467268

M. Hind, Pointer analysis, Proceedings of the 2001 ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering , PASTE '01, pp.54-61, 2001.
DOI : 10.1145/379605.379665

H. Hong, Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination, Papers from the International Symposium on Symbolic and Algebraic Computation , ISSAC '92, pp.177-188, 1992.
DOI : 10.1145/143242.143306

H. Hong and M. S. Din, Variant quantifier elimination, Journal of Symbolic Computation, vol.47, issue.7, pp.883-901, 2012.
DOI : 10.1016/j.jsc.2011.05.014
URL : https://hal.archives-ouvertes.fr/hal-00778365

F. Irigoin and R. Triolet, Supernode partitioning, Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages , POPL '88, pp.319-328, 1988.
DOI : 10.1145/73560.73588

A. Jimborean, Adapting the Polytope Model for Dynamic and Speculative Parallelization. Theses, pp.17-53, 2012.
DOI : 10.1145/2145816.2145861
URL : https://hal.archives-ouvertes.fr/tel-00733850

V. Kaplansky, Gcc patch: implementation of alias versioning in vectorizer, pp.53-82, 2006.

R. M. Karp, R. E. Miller, and S. Winograd, The Organization of Computations for Uniform Recurrence Equations, Journal of the ACM, vol.14, issue.3, pp.563-590, 1967.
DOI : 10.1145/321406.321418

L. Lamport, The parallel execution of DO loops, Communications of the ACM, vol.17, issue.2, pp.83-93, 1974.
DOI : 10.1145/360827.360844

J. M. Martinez-caamaño, Fast and Flexible Compilation Techniques for Effective Speculative Polyhedral Parallelization. Theses, p.53, 2016.

V. Maslov, Delinearization: An efficient way to break multiloop dependence equations, Proceedings of the ACM SIGPLAN 1992 Conference on Programming Language Design and Implementation , PLDI '92, pp.152-161, 1992.

N. Nethercote and J. Seward, How to shadow every byte of memory used by a program, Proceedings of the 3rd international conference on Virtual execution environments , VEE '07, pp.65-74, 2007.
DOI : 10.1145/1254810.1254820

D. Nuzman, R. Eres, R. Guenther, J. Jelinek, M. Matz et al., Autovectorization in gcc, p.53, 2003.

C. E. Oancea and L. Rauchwerger, Logical inference techniques for loop parallelization, Proceedings of the 33rd ACM SIGPLAN Conference on Programming Language Design and Implementation , PLDI '12, pp.509-520, 2012.
DOI : 10.1145/2254064.2254124

E. Park, J. Cavazos, L. Pouchet, C. Bastoul, A. Cohen et al., Predictive Modeling in a Polyhedral Optimization Space, International Journal of Parallel Programming, vol.18, issue.1, pp.704-750, 2013.
DOI : 10.1145/1088149.1088168
URL : https://hal.archives-ouvertes.fr/hal-00918653

H. Pirk, E. Petraki, S. Idreos, S. Manegold, and M. L. Kersten, Database cracking, Proceedings of the Tenth International Workshop on Data Management on New Hardware, DaMoN '14, pp.1-4, 2014.
DOI : 10.1145/2619228.2619232
URL : https://ir.cwi.nl/pub/22474/22474D.pdf

S. Pop, A. Cohen, C. Bastoul, S. Girbal, G. Silber et al., Graphite: Polyhedral analyses and optimizations for gcc, Proceedings of the 2006 GCC Developers Summit, pp.2006-2023, 2006.

S. Pop, A. Cohen, and G. Silber, Induction Variable Analysis with Delayed Abstractions, High Performance Embedded Architectures and Compilers, pp.218-232, 2005.
DOI : 10.1007/11587514_15
URL : https://hal.archives-ouvertes.fr/hal-01257294

L. Pouchet, PoCC, the Polyhedral Compiler Collection, version 1.3, 2010.

W. Pugh, The Omega test: a fast and practical integer programming algorithm for dependence analysis, Proceedings of the 1991 ACM/IEEE conference on Supercomputing , Supercomputing '91, pp.4-13, 1991.
DOI : 10.1145/125826.125848

W. Pugh and D. Wonnacott, Non-Linear Array Dependence Analysis, Languages, Compilers and Run-Time Systems for Scalable Computers, pp.1-14, 1996.
DOI : 10.1007/978-1-4615-2315-4_1
URL : http://www.cs.umd.edu/Library/TRs/CS-TR-3372/CS-TR-3372.ps.Z

S. Rus, L. Rauchwerger, and J. Hoeflinger, Hybrid analysis, Proceedings of the 16th international conference on Supercomputing , ICS '02, pp.251-283, 2002.
DOI : 10.1145/514191.514229

M. Schweighofer, An algorithmic approach to Schm??dgen's Positivstellensatz, Journal of Pure and Applied Algebra, vol.166, issue.3, pp.307-319, 2002.
DOI : 10.1016/S0022-4049(01)00041-X
URL : https://doi.org/10.1016/s0022-4049(01)00041-x

Y. Smaragdakis and G. Balatsouras, Pointer analysis. Found. Trends Program, Lang, vol.2, issue.1, pp.1-69, 2015.

A. Sukumaran-rajam, Beyond the Realm of the Polyhedral Model: Combining Speculative Program Parallelization with Polyhedral Compilation. Theses, p.53, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01251748

A. Sukumaran-rajam, J. M. Martinez, W. Wolff, A. Jimborean, C. et al., Speculative Program Parallelization with Scalable and Decentralized Runtime Verification, Runtime Verification, pp.124-139, 2014.
DOI : 10.1007/978-3-319-11164-3_11
URL : https://hal.archives-ouvertes.fr/hal-01070610

P. A. Suriana, Fourier-motzkin with non-linear symbolic constant coefficients. Master's thesis, Massachusetts Institute of Technology, p.51, 2016.

H. Sutter, The free lunch is over: A fundamental turn toward concurrency in software, 2005.

K. Trifunovic, A. Cohen, D. Edelsohn, F. Li, T. Grosser et al., Graphite two years after: First lessons learned from real-world polyhedral compilation, GCC Research Opportunities Workshop, p.17, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00551516

R. A. Van-engelen, J. Birch, Y. Shou, B. Walsh, and K. A. Gallivan, A unified framework for nonlinear dependence testing and symbolic analysis, Proceedings of the 18th annual international conference on Supercomputing , ICS '04, pp.106-115, 2004.
DOI : 10.1145/1006209.1006226

A. Venkat, M. Shantharam, M. Hall, and M. M. Strout, Non-affine Extensions to Polyhedral Code Generation, Proceedings of Annual IEEE/ACM International Symposium on Code Generation and Optimization, CGO '14, pp.185-185, 2014.
DOI : 10.1145/2581122.2544141

S. Verdoolaege, isl: An Integer Set Library for the Polyhedral Model, Mathematical Software? ICMS 2010, pp.299-302, 2010.
DOI : 10.1007/978-3-642-15582-6_49

S. Verdoolaege, R. Seghir, K. Beyls, V. Loechner, and M. Bruynooghe, Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions, Algorithmica, vol.48, issue.1, pp.37-66, 2007.
DOI : 10.1007/s00453-006-1231-0

S. Vijay, B. Bard, P. Igor, T. Olivier, D. et al., X10 language specification, 2016.

S. Williams, A. Waterman, and D. A. Patterson, Roofline, Communications of the ACM, vol.52, issue.4, pp.65-76, 2009.
DOI : 10.1145/1498765.1498785

W. A. Wulf and S. A. Mckee, Hitting the memory wall, ACM SIGARCH Computer Architecture News, vol.23, issue.1, pp.20-24, 1995.
DOI : 10.1145/216585.216588
URL : http://arxiv.org/pdf/1709.10008