) de cette méthodologie peuventêtrepeuventêtre obtenuesàobtenues`obtenuesà l'aide de résultats mathématiques comme les bornes de Cauchy [BPR03]. Cette méthodologie nous semble, avec le recul, extrêmement na¨?vena¨?ve. Tout d'abord, il faut noter que cette méthodologie suppose que l'on peut toujours obtenir un invariant non-linéaire ,
Inferring Min and Max Invariants Using Max-Plus Polyhedra, Proceedings of the 15th International Static Analysis Symposium Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS'10) Journal of Combinatorial Theory, series A. To appear. 96 [AJL] Mathias Argoud, Bertrand Jeannet, and Gaël La- lire. The concurinterproc analyzer 13th Symposium on Logic in Computer Science (LICS'98), pp.189-204, 1998. ,
DOI : 10.1007/978-3-540-69166-2_13
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.5698
Static analysis of memory manipulations by abstract interpretation ? Algorithmics of tropical polyhedra, and application to abstract interpretation A Semiring-based Quantitative Analysis of Mobile Systems, Electronic Notes in Theoretical Computer Science, vol.157, issue.1, pp.963-984, 2006. ,
Galois Connections and Fixed Point Calculus, Lecture Notes in Computer Science, vol.2297, issue.21, pp.89-148, 2000. ,
DOI : 10.1007/3-540-47797-7_4
An algorithm for finding all vertices of convex polyhedral sets, Journal of the Society for Industrial and Applied Mathematics, vol.9, issue.1, pp.72-88, 1961. ,
Synchronization and Linearity Abstracting soft constraints : framework, properties, examples Analysis and Prediction of the Long-Run Behavior of Probabilistic Sequential Programs with Recursion (Extended Abstract), FOCS '05 : Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science, pp.95175-211, 1992. ,
Semiring-based constraint satisfaction and optimization, POPL, pp.201-236, 1977. ,
DOI : 10.1145/256303.256306
Systematic Design of Program Analysis Frameworks Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation, 6th POPL PLILP'92, pp.269-282, 1979. ,
Abstract interpretation and application to logic programs & 3) :103?179, 1992. 15, 21 [CC92c] Patrick Cousot and Radhia Cousot. Abstract interpretation frameworks Automatic discovery of linear restraints among variables of a program, POPL, pp.511-547, 1992. ,
Fast inference of polynomial invariants for imperative programs Long-run cost analysis by approximation of linear operators over dioids, Algebraic Methodology and Software Technology, 12th International Conference Proceedings, volume 5140 of Lecture Notes in Computer Science, pp.122-138, 2008. ,
Long-run cost analysis by approximation of linear operators over dioids, Mathematical Structures in Computer Science, vol.20, issue.04, pp.589-624, 2010. ,
DOI : 10.1093/logcom/exi008
URL : https://hal.archives-ouvertes.fr/hal-00699608
Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics An introduction to computational algebraic geometry and commutative algebra. 103, 104 [Cou81] P. Cousot. Semantic foundations of program analysis, Program Flow Analysis, p.35, 1981. ,
Linear Invariant Generation Using Non-linear Constraint Solving, Lecture Notes in Computer Science, vol.2725, issue.100, pp.420-432, 2003. ,
DOI : 10.1007/978-3-540-45069-6_39
A Basic Calculus for Modelling Service Level Agreements, Bibliographie tral Elements in Max-Plus Algebra Proceedings of the IFAC Conference on System Structure and ControlDFM + 05 International Conference on Coordination Models and Languages, pp.95-128, 1998. ,
Probabilistic ??-calculus and Quantitative Program Analysis, Journal of Logic and Computation, vol.15, issue.2, pp.159-179, 2005. ,
DOI : 10.1093/logcom/exi008
Introduction to Lattices and Order Endomorphisms of semimodules over semirings with an idempotent operation, preprint of the mathematical institute of ukrainian academy of sciences : Endomorphisms of Finitely Generated Free Semimodules, Discipline of Programming Idempotent Analysis (Advances in Soviet Mathematics, pp.35-65, 1976. ,
Endomorphisms of finitely generated free semimodules, In Idempotent analysis Adv. in Sov. Math. AMS, RI, vol.60, issue.13, pp.63-92, 1987. ,
Concurrent Constraint Programming : Towards Probabilistic Abstract Interpretation, Principles and Practice of Declarative Programming, pp.127-138, 2000. ,
A Primer on Galois Connections, Annals of the New York Academy of Sciences, vol.12, issue.1 Papers on Gen, p.76, 1992. ,
DOI : 10.1016/0304-3975(78)90040-3
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5) Assigning meaning to programs, ISSAC Proc. Symp. in Applied Mathematics, pp.75-83, 1967. ,
Graphes, dio¨?desdio¨?des et semianneaux, Tec & Doc, vol.56, pp.42-76, 2001. ,
SPEED, ACM SIGPLAN Notices, vol.44, issue.1, pp.127-139, 2009. ,
DOI : 10.1145/1594834.1480898
An axiomatic basis for computer programming, CACM : Communications of the ACM, vol.12, pp.31-35, 1969. ,
SHReQ: coordinating application level QoS, Third IEEE International Conference on Software Engineering and Formal Methods (SEFM'05), pp.425-434, 2005. ,
DOI : 10.1109/SEFM.2005.40
Affine relationships among variables of a program, Acta Informatica, vol.6, issue.2 ,
DOI : 10.1007/BF00268497
Monotone data flow analysis frameworks AC- TAINF : Acta Informatica Recherche d'un système générateur minimal d'un polyhedre convexe, Thèse detroisì eme cycle, pp.36-55, 1966. ,
Coinductive big-step operational semantics . Information and Computation, p.130, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00309010
Weakly Relational Numerical Abstract Domains, The octagon abstract domain. Higher-Order and Symbolic Computation, pp.9231-100, 2004. ,
The complexity of the word problem for commutative semigroups and polynomial ideals, Advances in Mathematics, vol.46, issue.101, pp.305-329, 1982. ,
Interprocedurally Analyzing Polynomial Identities, STACS 2006, 23rd Annual Symposium on Theoretical Aspects of Computer Science ProceedingsMOS02] Markus Müller-Olm and Helmut Seidl. Polynomial constants are decidable. In SAS, pp.50-67, 2002. ,
DOI : 10.1007/11672142_3
Berechnung von polynomiellen Invarianten, p.142, 2004. ,
Inferring polynomial program invariants with polyinvar. Short paper, NSAD, p.144, 2005. ,
Automatic generation of polynomial loop invariants : algebraic foundations, ISSAC, pp.266-273, 2004. ,
Automatic generation of polynomial invariants of bounded degree using abstract interpretation, Science of Computer Programming, vol.64, issue.153, pp.54-75, 2007. ,
Generating all polynomial invariants in simple loops Classes of recursively enumerable sets and their decision problems. Transactions of the Managing quality of service with soft constraints Quantitative Static Analysis over Semirings : Analysing Cache Behaviour for Java Card, AAAI'08 : Proceedings of the 23rd national conference on Artificial intelligence QAPL06, Quantitative Aspects of Programming Languages, pp.443-476, 1953. ,
Constraint-Based Linear-Relations Analysis, Lecture Notes in Computer Science, vol.3148, issue.100, pp.53-68, 2004. ,
DOI : 10.1007/978-3-540-27864-1_7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.114.8736
Nonlinear loop invariant generation using Gröbner bases, POPL, pp.318-329, 2004. ,
The Formal Semantics of Programming Languages, p.105, 1993. ,