How good are convex hull algorithms?, Computational Geometry, vol.7, issue.5-6, pp.265-301, 1997. ,
DOI : 10.1016/S0925-7721(96)00023-5
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra, Discrete & Computational Geometry, vol.8, issue.3, pp.295-313, 1992. ,
DOI : 10.1007/BF02293050
Reverse search for enumeration, Discrete Applied Mathematics, vol.65, issue.1-3, pp.21-46, 1996. ,
DOI : 10.1016/0166-218X(95)00026-N
Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach, Theoretical Computer Science, 7th Italian Conference, ICTCS 2001, Proceedings, volume 2202 of Lecture Notes in Computer Science, pp.312-327, 2001. ,
DOI : 10.1007/3-540-45446-2_20
Decremental maintenance of reachability in hypergraphs and minimum models of horn formulae, Algorithms and Computation, 8th International Symposium, ISAAC '97 Proceedings, volume 1350 of Lecture Notes in Computer Science, pp.122-131, 1997. ,
DOI : 10.1007/3-540-63890-3_14
Inferring Min and Max Invariants Using Max-Plus Polyhedra, SAS'08, pp.189-204, 2008. ,
DOI : 10.1007/978-3-540-69166-2_13
Tropical polyhedra are equivalent to mean payoff games. preprint, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00778078
Computing the Extreme Points of Tropical Polyhedra. arXiv:math/0904, 2009. ,
The Tropical Double Description Method, Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS'10), 2010. ,
Static Analysis of String Manipulations in Critical Embedded C Programs, Static Analysis, 13th International Symposium (SAS'06), pp.35-51, 2006. ,
DOI : 10.1007/11823230_4
Set coverings and invertibility of functional Galois connections, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, pp.19-51, 2005. ,
DOI : 10.1090/conm/377/06983
URL : https://hal.archives-ouvertes.fr/inria-00000966
The number of extreme points of tropical polyhedra, Journal of Combinatorial Theory, Series A, vol.118, issue.1, 2010. ,
DOI : 10.1016/j.jcta.2010.04.003
Analyse Statique par Interprétation Abstraite : ApplicationàApplicationà la Détection de Dépassement de Tampon, ` eme Symposium sur la Sécurité des Technologies de l'Information et des Communications (SSTIC'07), pp.347-384, 2007. ,
Static analysis by abstract interpretation: application to the detection of heap overflows, Journal in Computer Virology, vol.5, issue.3, pp.5-23, 2008. ,
DOI : 10.1007/s11416-007-0063-z
Data Structures and Algorithms, 1983. ,
On-line algorithms for polynomially solvable satisfiability problems, The Journal of Logic Programming, vol.10, issue.1, pp.69-90509, 1978. ,
DOI : 10.1016/0743-1066(91)90006-B
Non-disjunctive Numerical Domain for Array Predicate Abstraction, Programming Languages and Systems , 17th European Symposium on Programming Proceedings, pp.163-177, 2008. ,
DOI : 10.1007/978-3-540-78739-6_14
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.592.1207
TPLib: Tropical polyhedra library, 2009. ,
DOI : 10.1016/j.jcta.2013.01.011
URL : http://arxiv.org/abs/1205.6314
Introduction to max-linear programming, IMA Journal of Management Mathematics, vol.20, issue.3, 2008. ,
DOI : 10.1093/imaman/dpn029
Sorting networks and their applications, Proceedings of the AFIPS Spring Joint Computer Conference 32, pp.307-314, 1968. ,
A static analyzer for large safety-critical software, ACM SIGPLAN PLDI'03, pp.196-207, 2003. ,
Shape Analysis for Composite Data Structures, Proceedings of the 19th International Conference on Computer Aided Verification, 2007. ,
DOI : 10.1007/978-3-540-73368-3_22
Shape Analysis for Composite Data Structures, Proceedings of the 19th International Conference on Computer Aided Verification, 2007. ,
DOI : 10.1007/978-3-540-73368-3_22
Synchronization and Linearity, 1992. ,
An elimination method for finding all solutions of the system of linear equations over an extremal algebra, Ekonomickomatematicky Obzor, vol.20, 1984. ,
B-convexity. Optimization, pp.103-127, 2004. ,
Path invariants, PLDI '07: Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation, pp.300-309, 2007. ,
Separation in B-convexity, Pacific Journal of Optimization, vol.1, pp.13-30, 2005. ,
Precise Widening Operators for Convex Polyhedra, Static Analysis: Proceedings of the 10th International Symposium Proceedings of the 18th International Conference on Computer Aided Verification, pp.337-354, 2003. ,
DOI : 10.1007/3-540-44898-5_19
Widening operators for powerset domains. Software Tools for Technology Transfer, pp.449-466, 2006. ,
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. ,
DOI : 10.1016/j.scico.2007.08.001
Automatic predicate abstraction of C programs, ACM SIGPLAN Notices, vol.36, issue.5, pp.203-213, 2001. ,
DOI : 10.1145/381694.378846
Exponential behaviour of the Butkovi?????Zimmermann algorithm for solving two-sided linear systems in max-algebra, Discrete Applied Mathematics, vol.156, issue.18, pp.3506-3509, 2008. ,
DOI : 10.1016/j.dam.2008.03.016
The Max-Atom Problem and Its Relevance, Logic for Programming, Artificial Intelligence, and Reasoning , 15th International Conference, pp.47-61, 2008. ,
DOI : 10.1007/978-3-540-89439-1_4
Generators, extremals and bases of max cones, Linear Algebra and its Applications, vol.421, issue.2-3, pp.394-406, 2007. ,
DOI : 10.1016/j.laa.2006.10.004
A strongly polynomial algorithm for solving two-sided linear systems in max-algebra, Discrete Applied Mathematics, vol.154, issue.3, pp.437-446, 2006. ,
DOI : 10.1016/j.dam.2005.09.008
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
Systematic design of program analysis frameworks, Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages , POPL '79, pp.269-282, 1979. ,
DOI : 10.1145/567752.567778
Abstract interpretation and application to logic programs, Journal of Logic Programming, vol.13, pp.2-3, 1992. ,
Abstract interpretation frameworks, Journal of Logic and Computation, vol.2, issue.4, pp.511-547, 1992. ,
The Octahedron Abstract Domain, Static Analysis Symposium (SAS), pp.312-327, 2004. ,
DOI : 10.1007/978-3-540-27864-1_23
The ASTRE?? Analyzer, Proceedings of the European Symposium on Programming (ESOP'05), pp.21-30, 2005. ,
DOI : 10.1007/978-3-540-31987-0_3
Points-to analysis, conditional soundness, and proving the absence of errors, Static Analysis Symposium (SAS), pp.62-77, 2008. ,
Automatic verification of finite-state concurrent systems using temporal logic specifications, ACM Transactions on Programming Languages and Systems, vol.8, issue.2, pp.244-263, 1986. ,
DOI : 10.1145/5397.5399
Projections in minimax algebra, Mathematical Programming, pp.111-123, 1976. ,
DOI : 10.1093/imamat/11.2.145
Minimax algebra, of Lecture Notes in Economics and Mathematical Systems, 1979. ,
DOI : 10.1007/978-3-642-48708-8
The equation A???x=B???y over (max,+), Theoretical Computer Science, vol.293, issue.1, pp.3-12, 2003. ,
DOI : 10.1016/S0304-3975(02)00228-1
Model checking and abstraction, ACM Transactions on Programming Languages and Systems, vol.16, issue.5, pp.1512-1542, 1994. ,
DOI : 10.1145/186025.186051
Maxplus toolbox of scilab Available at http://minimal.inria.fr/gaubert/maxplustoolbox ,
Max-plus algebra and system theory: Where we are and where to go now, Annual Reviews in Control, vol.23, pp.207-219, 1999. ,
DOI : 10.1016/S1367-5788(99)90091-3
Hahn-Banach separation theorem for max-plus semimodules, Optimal Control and Partial Differential Equations, pp.325-334, 2001. ,
Duality and separation theorems in idempotent semimodules, Linear Algebra and its Applications, vol.379, pp.395-422, 2004. ,
DOI : 10.1016/j.laa.2003.08.010
URL : https://hal.archives-ouvertes.fr/inria-00071917
Max-plus convex sets and functions, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, pp.105-129, 2005. ,
DOI : 10.1090/conm/377/06987
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
An optimal convex hull algorithm in any fixed dimension. Discrete and Compututational Geometry, pp.377-409, 1993. ,
Algorithm for discovering the set of all solutions of a linear programming problem, U.S.S.R. Computational Mathematics and Mathematical Physics, vol.8, issue.6, pp.282-293, 1968. ,
The porta library ,
Algorithms for dense graphs and networks on the random access computer, Algorithmica, vol.1, issue.1, pp.521-549, 1996. ,
DOI : 10.1007/BF01940880
Verification by abstract interpretation, Proc. Int. Symp. on Verification ? Theory & Practice ? Honoring Zohar Manna's 64th Birthday, pp.243-268, 2003. ,
Introduction to Algorithms, 2001. ,
Linear Programming and Extensions, 1963. ,
A storeless model of aliasing and its abstractions using finite representations of right-regular equivalence relations, ICCL'92, Proceedings of the 1992 International Conference on Computer Languages, pp.2-13, 1992. ,
Interprocedural may-alias analysis for pointers: beyond klimiting, PLDI '94: Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation, pp.230-241, 1994. ,
DOI : 10.1145/773473.178263
Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems, SIAM Journal on Control and Optimization, vol.48, issue.8, 2009. ,
DOI : 10.1137/090747191
URL : https://hal.archives-ouvertes.fr/hal-00562586
A Local Shape Analysis Based on Separation Logic, Tools and Algorithms for the Construction and Analysis of Systems, 12th International Conference, pp.287-302, 2006. ,
DOI : 10.1145/514188.514190
Cssv: towards a realistic tool for statically detecting all buffer overflows in C, PLDI '03: Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation, pp.155-167, 2003. ,
Tropical convexity, Doc. Math, vol.9, pp.1-27, 2004. ,
Tropical Polytopes and Cellular Resolutions, Experimental Mathematics, vol.16, issue.3, pp.277-292, 2007. ,
DOI : 10.1080/10586458.2007.10129009
URL : http://arxiv.org/abs/math/0605494
Orna Grumberg, and Doron A. Peled. Model checking, 1999. ,
With microscope and tweezers: An analysis of the internet virus of november 1988, IEEE Symposium on, p.326, 1989. ,
Why: a multi-language multi-prover verification tool, Research Report, vol.1366, 2003. ,
Implementation of hash sets for OCaml, 2008. ,
Double description method revisited, Selected papers from the 8th Franco-Japanese and 4th Franco-Chinese Conference on Combinatorics and Computer Science, pp.91-111, 1996. ,
DOI : 10.1007/3-540-61576-8_77
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.8343
Predicate abstraction for software verification, POPL '02: Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp.191-202, 2002. ,
The cdd library ,
Path-based depth-first search for strong and biconnected components, Inf. Process. Lett, vol.74, issue.3-4, pp.107-114, 2000. ,
Big Code, 2005. ,
Théorie des systèmes linéaires dans les dio¨?desdio¨?des, Thèse, ´ Ecole des Mines de Paris, 1992. ,
A numerical abstract domain based on expression abstraction and max operator with application in timing analysis, Computer Aided Verification, 20th International Conference, pp.370-384, 2008. ,
Max Horn SAT and the minimum cut problem in directed hypergraphs, Mathematical Programming, vol.1, issue.3, pp.213-237, 1998. ,
DOI : 10.1007/BF01581727
Max-Plus Convex Geometry, Lecture Notes in Comput. Sci, vol.4136, pp.192-206, 2006. ,
DOI : 10.1007/11828563_13
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.7868
The Minkowski theorem for max-plus convex sets, Linear Algebra and its Applications, vol.421, issue.2-3, pp.356-369, 2007. ,
DOI : 10.1016/j.laa.2006.09.019
URL : https://hal.archives-ouvertes.fr/inria-00071358
The tropical analogue of polar cones, Linear Algebra and Appl, vol.431, pp.608-625, 2009. ,
Minimal half-spaces and external representation of tropical polyhedra, Journal of Algebraic Combinatorics, vol.13, issue.2, 2009. ,
DOI : 10.1007/s10801-010-0246-4
Directed hypergraphs and applications, Discrete Applied Mathematics, vol.42, issue.2-3, pp.177-201, 1993. ,
DOI : 10.1016/0166-218X(93)90045-P
Lifting abstract interpreters to quantified logical domains, POPL'08: Proceedings of the 35th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, 2008. ,
Methods and applications of (max,+) linear algebra, STACS'97 number 1200, 1997. ,
DOI : 10.1007/BFb0023465
URL : https://hal.archives-ouvertes.fr/inria-00073603
Static Analysis of Numerical Algorithms, Static Analysis, 13th International Symposium (SAS'06), pp.18-5134, 2006. ,
DOI : 10.1007/11823230_3
Optimal domains for disjunctive abstract interpretation, Science of Computer Programming, vol.32, issue.1-3, pp.1-3177, 1998. ,
DOI : 10.1016/S0167-6423(97)00034-8
Static analysis of linear congruence equalities among variables of a program, International Joint Conference on Theory and Practice of Software Development, pp.169-192, 1991. ,
DOI : 10.1007/3-540-53982-4_10
Static analyses of congruence properties on rational numbers (extended abstract), Static Analysis Symposium (SAS), pp.278-292, 1997. ,
DOI : 10.1007/BFb0032748
A framework for numeric analysis of array operations, ACM SIGPLAN Notices, vol.40, issue.1, pp.338-350, 2005. ,
DOI : 10.1145/1047659.1040333
Combining abstract interpreters, PLDI '06: Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation, pp.376-386, 2006. ,
DOI : 10.1145/1133255.1134026
Détermination Automatique de Relations Linéaires Vérifiées par les Variables d'un Programme, Thèse de 3 ` eme cycle d'informatique, 1979. ,
Doubleplussimple Minilang for Goodthinkful Static Analysis of C, 2008. ,
Discovering properties about arrays in simple programs, Proceedings of the ACM SIGPLAN 2008 Conference on Programming Language Design and Implementation, pp.339-348, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00288274
Refining Static Analyses by Trace-Based Partitioning Using Control Flow, Static Analysis, 5th International Symposium, SAS '98, pp.200-214, 1998. ,
DOI : 10.1007/3-540-49727-7_12
Taming False Alarms from a Domain-Unaware C Analyzer by a Bayesian Statistical Post Analysis, Static Analysis: 12th International Symposium, SAS 2005. Proceedings, Lecture Notes in Computer Science, pp.203-217, 2005. ,
DOI : 10.1007/11547662_15
APRON numerical abstract domain library ,
Array Abstractions from Proofs, CAV, pp.193-206, 2007. ,
DOI : 10.1007/978-3-540-73368-3_23
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.8283
Tropical halfspaces, Combinatorial and computational geometry, pp.409-431, 2005. ,
Tropical convex hull computations, 2008. ,
DOI : 10.1090/conm/495/09698
URL : http://arxiv.org/abs/0809.4694
Streamlined development of body electronics systems using model-based design, 2006. ,
Affine relationships among variables of a program, Acta Informatica, vol.6, issue.2, pp.133-151, 1976. ,
DOI : 10.1007/BF00268497
Max-plus (A, B)-invariant spaces and control of timed discrete event systems, IEEE Trans. Aut. Control, vol.52, issue.2, pp.229-241, 2007. ,
Generating all vertices of a polyhedron is hard, SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pp.758-765, 2006. ,
A unified approach to global program optimization, POPL, pp.194-206, 1973. ,
Ariane 5, flight 501 failure, report by the inquiry board, 1996. ,
Simple linear-time algorithms for minimal fixed points (extended abstract), Automata, Languages and Programming, 25th International Colloquium, ICALP'98, Proceedings, volume 1443 of Lecture Notes in Computer Science, pp.53-66, 1998. ,
A note on Chernikova's algorithm, 1992. ,
The Build Master: Microsoft's Software Configuration Management Best Practices, 2005. ,
Code Complete, Second Edition, 2004. ,
The maximum numbers of faces of a convex polytope, Mathematika, vol.17, pp.179-184, 1970. ,
A new numerical abstract domain based on difference-bound matrices, PADO II, pp.155-172, 2001. ,
The octagon abstract domain, AST, pp.310-319, 2001. ,
Weakly Relational Numerical Abstract Domains, 2004. ,
Field-sensitive value analysis of embedded C programs with union types and pointer arithmetics, ACM SIGPLAN LCTES'06, pp.54-63, 2006. ,
The pitfalls of verifying floating-point computations, ACM Transactions on Programming Languages and Systems, vol.30, issue.3, p.12, 2008. ,
DOI : 10.1145/1353445.1353446
URL : https://hal.archives-ouvertes.fr/hal-00128124
A Note on Karr???s Algorithm, Lecture Notes in Computer Science, vol.3142, pp.1016-1028, 2004. ,
DOI : 10.1007/978-3-540-27836-8_85
Trace Partitioning in Abstract Interpretation Based Static Analyzers, European Symposium on Programming (ESOP'05), pp.5-20, 2005. ,
DOI : 10.1007/978-3-540-31987-0_2
3. The Double Description Method, Contributions to the Theory of Games, volume II, pp.51-73, 1953. ,
DOI : 10.1515/9781400881970-004
Problem-Solving Methods in Artificial Intelligence, 1971. ,
CIL: Intermediate language and tools for analysis and transformation of C programs, CC '02: Proceedings of the 11th International Conference on Compiler Construction, pp.213-228, 2002. ,
Simplification by Cooperating Decision Procedures, ACM Transactions on Programming Languages and Systems, vol.1, issue.2, pp.245-257, 1979. ,
DOI : 10.1145/357073.357079
Hyperpaths and shortest hyperpaths, COMO '86: Lectures given at the third session of the Centro Internazionale Matematico Estivo (C.I.M.E.) on Combinatorial optimization. [NPG98] Sang Nguyen, Stefano Pallottino, and Michel Gendreau. Implicit enumeration of hyperpaths in a logit model for transit networks, pp.258-27154, 1989. ,
DOI : 10.1007/BFb0083470
Max-plus convex sets and max-plus semispaces. I. Optimization, pp.171-205, 2007. ,
DOI : 10.1080/02331930600819852
On finding hypercycles in chemical reaction networks, Appl. Math. Lett, vol.21, issue.9, pp.881-884, 2008. ,
Tropical semirings, Plo81] G. D. Plotkin. A structural approach to operational semantics, pp.50-69, 1981. ,
DOI : 10.1017/CBO9780511662508.004
A directed hypergraph model for random time dependent shortest paths, European Journal of Operational Research, vol.123, issue.2, pp.315-324, 2000. ,
DOI : 10.1016/S0377-2217(99)00259-3
Hypergraph Reductions and Satisfiability Problems, Theory and Applications of Satisfiability Testing, 6th International Conference, SAT 2003, pp.383-397, 2003. ,
DOI : 10.1007/978-3-540-24605-3_29
First steps in tropical geometry, Idempotent mathematics and mathematical physics, pp.289-317, 2005. ,
DOI : 10.1090/conm/377/06998
On completely recursively enumerable classes and their key arrays, J. Symb. Log, vol.21, issue.3, pp.304-308, 1956. ,
Software development for the Boeing 777, 1996. ,
The trace partitioning abstract domain, ACM Transactions on Programming Languages and Systems, vol.29, issue.5, 2007. ,
DOI : 10.1145/1275497.1275501
Top 25 most dangerous programming errors, 2007. ,
A convex hull algorithm optimal for point sets in even dimensions, 1981. ,
Abstract convex analysis, 1997. ,
Analyzing String Buffers in C, Algebraic Methodology and Software Technology, pp.365-379, 2002. ,
DOI : 10.1007/3-540-45719-4_25
Two Variables per Linear Inequality as an Abstract Domain Logic-Based Program Synthesis and Transformation, LNCS, vol.2664, pp.71-89, 2003. ,
Solving shape-analysis problems in languages with destructive updating, ACM Transactions on Programming Languages and Systems, vol.20, issue.1, pp.1-50, 1998. ,
DOI : 10.1145/271510.271517
Parametric shape analysis via 3?valued logic, Symposium on Principles of Programming Languages, pp.105-118, 1999. ,
DOI : 10.1145/514188.514190
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.3161
Scalable Analysis of Linear Systems Using Mathematical Programming, Proceedings of VMCAI, volume 3385, 2005. ,
DOI : 10.1007/978-3-540-30579-8_2
Points-to analysis in almost linear time, Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages , POPL '96, pp.32-41, 1996. ,
DOI : 10.1145/237721.237727
A lattice-theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics, vol.5, issue.2, pp.285-309, 1955. ,
DOI : 10.2140/pjm.1955.5.285
Depth-First Search and Linear Graph Algorithms, SIAM Journal on Computing, vol.1, issue.2, pp.146-160, 1972. ,
DOI : 10.1137/0201010
Principle of database systems, Computer Science Press, 1982. ,
Precise and efficient static array bound checking for large embedded C programs, PLDI '04: Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation, pp.231-242, 2004. ,
Nonuniform Alias Analysis of Recursive Data Structures and Arrays, SAS '02: Proceedings of the 9th International Symposium on Static Analysis, pp.36-51, 2002. ,
DOI : 10.1007/3-540-45789-5_6
A Scalable Nonuniform Pointer Analysis for Embedded Programs, Static Analysis, 11th International Symposium, SAS 2004, pp.149-164, 2004. ,
DOI : 10.1007/978-3-540-27864-1_13
Extremal algebra of positive matrices, Elektron. Informationsverarbeitung und Kybernetik, vol.3, pp.39-71, 1967. ,
Lectures on Polytopes, 1998. ,
Lectures on 0/1-polytopes, Polytopes ? combinatorics and computation (Oberwolfach, pp.1-41, 1997. ,
A general separation theorem in extremal algebras, Ekonom.- Mat. Obzor, vol.13, issue.2, pp.179-201, 1977. ,