Bibliography

Major publications by the team in recent years

• 1M. Akian.
  Densities of idempotent measures and large deviations, in: Transactions of the American Mathematical Society, 1999, vol. 351, n^o 11, pp. 4515–4543.
• 2M. Akian, R. Bapat, S. Gaubert.
  Max-plus algebras, in: Handbook of Linear Algebra (Discrete Mathematics and Its Applications), L. Hogben (editor), Chapman & Hall/CRC, 2006, vol. 39, Chapter 25.
• 3M. Akian, S. Gaubert.
  Spectral Theorem for Convex Monotone Homogeneous Maps, and ergodic Control, in: Nonlinear Analysis. Theory, Methods & Applications, 2003, vol. 52, n^o 2, pp. 637-679.
  http://hal.inria.fr/inria-00000201/en/
• 4M. Akian, S. Gaubert, B. Lemmens, R. Nussbaum.
  Iteration of order preserving subhomogeneous maps on a cone, in: Math. Proc. Cambridge Philos. Soc., 2006, vol. 140, n^o 1, pp. 157–176.
  http://www.arxiv.org/abs/math.DS/0410084
• 5M. Akian, A. Sulem, M. Taksar.
  Dynamic optimisation of long term growth rate for a portfolio with transaction costs and logarithmic utility, in: Mathematical Finance, 2001, vol. 11, n^o 2, pp. 153–188.
• 6F. Baccelli, G. Cohen, G. Olsder, J.-P. Quadrat.
  Synchronisation and Linearity, Wiley, 1992.
• 7J. Cochet-Terrasson, S. Gaubert, J. Gunawardena.
  A constructive fixed point theorem for min-max functions, in: Dynamics and Stability of Systems, 1999, vol. 14, n^o 4.
• 8G. Cohen, S. Gaubert, J.-P. Quadrat.
  Duality and Separation Theorems in Idempotent Semimodules, in: Linear Algebra and Appl., 2004, vol. 379, pp. 395–422.
  http://arxiv.org/abs/math.FA/0212294
• 9G. Cohen, S. Gaubert, J.-P. Quadrat.
  Max-plus algebra and system theory: where we are and where to go now, in: Annual Reviews in Control, 1999, vol. 23, pp. 207–219.
• 10S. Gaubert, J. Gunawardena.
  The Perron-Frobenius Theorem for Homogeneous, Monotone Functions, in: Trans. of AMS, 2004, vol. 356, n^o 12, pp. 4931-4950.
  http://www.ams.org/tran/2004-356-12/S0002-9947-04-03470-1/home.html

Publications of the year

Articles in International Peer-Reviewed Journals

• 11A. Adjé, S. Gaubert, E. Goubault.
  Computing the smallest fixed point of order-preserving nonexpansive mappings arising in positive stochastic games and static analysis of programs, in: Journal of Mathematical Analysis and applications, February 2014, vol. 410, n^o 1, pp. 227-240, Also arXiv:0806.1160. [ DOI : 10.1016/j.jmaa.2013.07.076 ]
  https://hal.archives-ouvertes.fr/hal-00940804
• 12M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for eigenvalues of matrices, in: Linear Algebra and its Applications, April 2014, vol. 446, pp. 281–303, See also arXiv:1309.7319. [ DOI : 10.1016/j.laa.2013.12.021 ]
  https://hal.inria.fr/hal-00881205
• 13X. Allamigeon, A. Legay, U. Fahrenberg, R. Katz, S. Gaubert.
  Tropical Fourier–Motzkin elimination, with an application to real-time verification, in: International Journal of Algebra and Computation (IJAC), 2014, vol. 24, n^o 5, pp. 569 - 607. [ DOI : 10.1142/S0218196714500258 ]
  https://hal.inria.fr/hal-01087367
• 14F. Billy, J. Clairambault, O. Fercoq, S. Gaubert, T. Lepoutre, T. Ouillon, S. Saito.
  Synchronisation and control of proliferation in cycling cell population models with age structure, in: Mathematics and Computers in Simulation, February 2014, vol. 96, pp. 66-94. [ DOI : 10.1016/j.matcom.2012.03.005 ]
  https://hal.archives-ouvertes.fr/hal-00662885
• 15J. Bolte, S. Gaubert, G. Vigeral.
  Definable Zero-Sum Stochastic Games, in: Mathematics of Operations Research, 2014, pp. 1-29, Published online. [ DOI : 10.1287/moor.2014.0666 ]
  https://hal.archives-ouvertes.fr/hal-00777707
• 16S. Gaubert, Z. Qu.
  The contraction rate in Thompson part metric of order-preserving flows on a cone - application to generalized Riccati equations, in: Journal of Differential Equations, April 2014, vol. 256, n^o 8, pp. 2902-2948, Also arXiv:1206.0448. [ DOI : 10.1016/j.jde.2014.01.024 ]
  https://hal.inria.fr/hal-00783972
• 17S. Gaubert, Z. Qu.
  Dobrushin ergodicity coefficient for Markov operators on cones, in: Integral Equations and Operator Theory, January 2015, vol. 1, n^o 81, pp. 127-150, Also arXiv:1307.4649. [ DOI : 10.1007/s00020-014-2193-2 ]
  https://hal.inria.fr/hal-01099179
• 18V. Magron, X. Allamigeon, S. Gaubert, B. Werner.
  Certification of real inequalities: templates and sums of squares, in: Mathematical Programming B, November 2014, 30 p, Also arXiv:1403.5899. [ DOI : 10.1007/s10107-014-0834-5 ]
  https://hal.inria.fr/hal-01096485
• 19V. Magron, X. Allamigeon, S. Gaubert, B. Werner.
  Formal Proofs for Nonlinear Optimization, in: Journal of Formalized Reasoning, January 2015, vol. 8, n^o 15, pp. 1-24, Also ArXiv:1404.7282.
  https://hal.archives-ouvertes.fr/hal-00985675
• 20P. Poncet.
  Convexities on ordered structures have their Krein–Milman theorem, in: Journal of Convex Analysis, 2014, vol. 21, n^o 1, pp. 89–120, See also arXiv:1301.0760.
  https://hal.inria.fr/hal-00922374
• 21P. Poncet.
  The idempotent Radon–Nikodym theorem has a converse statement, in: Information Sciences, July 2014, n^o 271, pp. 115–124, See also arXiv:1301.0140. [ DOI : 10.1016/j.ins.2014.02.074 ]
  https://hal.inria.fr/hal-00922377
• 22Z. Qu.
  Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method, in: SIAM Journal on Control and Optimization, September 2014, vol. 52, n^o 5, pp. 2677-2709, Also arXiv:1301.4777. [ DOI : 10.1137/130906702 ]
  https://hal.inria.fr/hal-01112251

Invited Conferences

• 23M. Akian.
  Log-majorization of eigenvalues of matrix polynomials and tropical scaling, in: Structured Matrix Days, Limoges, France, May 2014.
  https://hal.inria.fr/hal-01104386
• 24S. Gaubert.
  From tropical linear algebra to zero-sum games, in: The 19th International Linear Algebra Society Conference, Seoul, South Korea, August 2014, Invited Plenary Talk.
  https://hal.inria.fr/hal-01112709

International Conferences with Proceedings

• 25M. Akian, S. Gaubert, A. Hochart.
  Generic uniqueness of the bias vector of mean payoff zero-sum games, in: 53rd IEEE Conference on Decision and Control, Los Angeles, United States, December 2014, See also arXiv:1411.1211.
  https://hal.inria.fr/hal-01095930
• 26X. Allamigeon, P. Benchimol, S. Gaubert.
  The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average, in: ICALP 2014, Copenhagen, France, J. Esparza, P. Fraigniaud, T. Husfeldt, E. Koutsoupias (editors), 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part I, Springer, July 2014, vol. 8572, 12 p. [ DOI : 10.1007/978-3-662-43948-7_8 ]
  https://hal.inria.fr/hal-01096447
• 27X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  La méthode du simplexe tropical, in: ROADEF - 15ème congrès annuel de la Société française de recherche opérationnelle et d’aide à la décision, Bordeaux, France, Société française de recherche opérationnelle et d’aide à la décision (ROADEF), February 2014, arxiv 1308.0454.
  https://hal.inria.fr/hal-01097726
• 28V. Calvez, P. Gabriel, S. Gaubert.
  Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems, in: IEEE 53rd Annual Conference on Decision and Control (CDC 2014), Los Angeles, United States, December 2014, pp. 1600–1607, Also arXiv:1404.1868.
  https://hal.archives-ouvertes.fr/hal-00974749
• 29S. Gaubert, Z. Qu, S. Sridharan.
  Bundle-based pruning in the max-plus curse of dimensionality free method, in: Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems, Groningen, Netherlands, July 2014, See also arXiv:1402.1436.
  https://hal.inria.fr/hal-01099175
• 30Z. Qu.
  A max-plus based randomized algorithm for solving a class of HJB PDEs, in: 53rd IEEE Conference on Decision and Control, Los Angeles, United States, Proceedings of the 53rd IEEE Conference on Decision and Control, IEEE, December 2014, pp. 1575–1580.
  https://hal.inria.fr/hal-01112264

Conferences without Proceedings

• 31M. Akian, S. Gaubert.
  Complexity of policy iteration for stochastic zero-sum games, in: PGMO-COPI'14, Paris-Saclay, France, October 2014.
  https://hal.inria.fr/hal-01104409
• 32M. Akian, S. Gaubert.
  Policy iteration for stochastic zero-sum games, in: NETCO, Tours, France, June 2014.
  https://hal.inria.fr/hal-01104405
• 33M. Akian, S. Gaubert, A. Hochart.
  Fixed Point Sets of Payment-Free Shapley Operators and Structural Properties of Mean Payoff Games, in: MTNS 2014, Groningen, Netherlands, July 2014.
  https://hal.inria.fr/hal-01112278
• 34M. Akian, S. Gaubert, A. Hochart.
  Generic uniqueness of the bias vector of mean-payoff zero-sum games, in: PGMO-COPI'14, Palaiseau, France, October 2014.
  https://hal.inria.fr/hal-01112285
• 35M. Akian, S. Gaubert, A. Hochart.
  Points fixes d’opérateur de Shapley sans paiement et propriétés structurelles des jeux à paiement moyen, in: MODE 2014, Rennes, France, March 2014.
  https://hal.inria.fr/hal-01112301
• 36M. Akian, S. Gaubert, J. Hook, A. Marchesini, F. Tisseur.
  Asymptotic eigenvalue problems, in: ILAS, Seoul, South Korea, August 2014.
  https://hal.inria.fr/hal-01112260
• 37M. Akian, S. Gaubert, A. Marchesini.
  Tropical bounds for eigenvalues of matrices using Hungarian dual variables, in: ILAS, Seoul, South Korea, August 2014.
  https://hal.inria.fr/hal-01104401
• 38M. Akian, P. Poncet.
  Krein–Milman's and Choquet's theorems in the max-plus world, in: Domains XI (International workshop on domain theory and applications), PARIS, France, September 2014.
  https://hal.inria.fr/hal-01112248
• 39X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial Simplex Algorithms Can Solve Mean Payoff Games, in: The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, July 2014.
  https://hal.inria.fr/hal-01097727
• 40X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial simplex algorithms can solve mean payoff games, in: 20th Conference of the International Federation of Operational Research Societies, Barcelone, Spain, July 2014.
  https://hal.inria.fr/hal-01097728
• 41X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Long and winding central paths, in: Recent Advances in Linear Optimization, Champs sur marne, France, July 2014.
  https://hal.inria.fr/hal-01097729

Scientific Books (or Scientific Book chapters)

• 42M. Akian, S. Gaubert, A. Guterman.
  Tropical Cramer Determinants Revisited, in: Tropical and Idempotent Mathematics and Applications, G. Litvinov, S. Sergeev (editors), Contemporary Mathematics, AMS, 2014, vol. 616, 45 p, See also arXiv:1309.6298.
  https://hal.inria.fr/hal-00881203
• 43C. Walsh.
  The horoboundary and isometry group of Thurston's Lipschitz metric, in: Handbook of Teichmüller Theory, Volume IV, A. Papadopoulos (editor), IRMA Lectures in Mathematics and Theoretical Physics, European Mathematical Society, May 2014, vol. 19, 838 p.
  https://hal.inria.fr/hal-01098838
• 44C. Walsh.
  The horofunction boundary and isometry group of the Hilbert geometry, in: Handbook of Hilbert Geometry, A. Papadopoulos, M. Troyanov (editors), IRMA Lectures in Mathematics and Theoretical Physics, European Mathematical Society, 2014, vol. 22.
  https://hal.inria.fr/hal-00782827

Scientific Popularization

• 45M. Akian.
  Policy iteration for stochastic zero-sum games, 2014, NETCO 2014, Parallel session/ slides.
  https://hal.inria.fr/hal-01024097

Other Publications

• 46M. Akian, S. Gaubert, A. Hochart.
  Ergodicity conditions for zero-sum games, May 2014, Preprint arXiv: 1405.4658, 30 pages.
  https://hal.inria.fr/hal-01096206
• 47M. Akian, S. Gaubert, A. Hochart.
  Fixed point of payment-free Shapley operators and structural properties of mean payoff games, June 2014, NETCO 2014, Poster.
  https://hal.inria.fr/hal-01112271
• 48M. Akian, S. Gaubert, A. Hochart.
  Fixed point of payment-free Shapley operators and structural properties of mean payoff games, June 2014, Mathematical Aspects of Game Theory and Applications (MAGTA 2014), Poster.
  https://hal.inria.fr/hal-01112660
• 49X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Combinatorial simplex algorithms can solve mean payoff games, 2014, Preprint arXiv:1309.5925, 15 pages, 3 figures. To appear in SIAM Journal on Optimization.
  https://hal.inria.fr/hal-00930915
• 50X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Long and winding central paths, May 2014, Preprint arXiv:1405.4161.
  https://hal.inria.fr/hal-01096452
• 51X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, 2014, Preprint arXiv:1308.0454, 35 pages, 7 figures, 4 algorithms. To appear in SIAM Journal on Discrete Mathematics.
  https://hal.inria.fr/hal-00930913
• 52X. Allamigeon, R. D. Katz.
  Tropicalization of facets of polytopes, August 2014, Preprint arXiv:1408.6176.
  https://hal.inria.fr/hal-01096435
• 53S. Gaubert, Z. Qu.
  Checking the strict positivity of Kraus maps is NP-hard, February 2014, Preprint arXiv:1402.1429.
  https://hal.inria.fr/hal-01097942

References in notes

• 54A. Neyman, S. Sorin (editors)
  Stochastic games and applications, NATO Science Series C: Mathematical and Physical Sciences, Kluwer Academic Publishers, Dordrecht, 2003, vol. 570, x+473 p.
• 55M. Akian, R. Bapat, S. Gaubert.
  Perturbation of eigenvalues of matrix pencils and optimal assignment problem, in: C. R. Acad. Sci. Paris, Série I, 2004, vol. 339, pp. 103–108.
  http://www.arxiv.org/abs/math.SP/0402438
• 56M. Akian, R. Bapat, S. Gaubert.
  Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem, 2005.
  http://arxiv.org/abs/math.SP/0402090
• 57M. Akian, R. Bapat, S. Gaubert.
  Asymptotics of the Perron Eigenvalue and Eigenvector using Max Algebra, in: C. R. Acad. Sci. Paris., 1998, vol. 327, Série I, pp. 927–932.
  http://hal.inria.fr/inria-00073240
• 58M. Akian, S. Gaubert.
  Policy iteration for perfect information stochastic mean payoff games with bounded first return times is strongly polynomial, 2013, Preprint arXiv:1310.4953, 17 pages.
  http://hal.inria.fr/hal-00881207
• 59M. Akian, S. Gaubert, A. Guterman.
  Tropical polyhedra are equivalent to mean payoff games, in: Internat. J. Algebra Comput., 2012, vol. 22, n^o 1, 1250001, 43 p. [ DOI : 10.1142/S0218196711006674 ]
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• 60M. Akian, S. Gaubert, V. Kolokoltsov.
  Set coverings and invertibility of functional Galois connections, in: Idempotent Mathematics and Mathematical Physics, G. Litvinov, V. Maslov (editors), Contemporary Mathematics, American Mathematical Society, 2005, pp. 19-51.
  http://arxiv.org/abs/math.FA/0403441
• 61M. Akian, S. Gaubert, V. Kolokoltsov.
  Solutions of max-plus linear equations and large deviations, in: Proceedings of the joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005 (CDC-ECC'05), Seville, Espagne, 2005.
  http://arxiv.org/abs/math.PR/0509279
• 62M. Akian, S. Gaubert, A. Lakhoua.
  The max-plus finite element method for solving deterministic optimal control problems: basic properties and convergence analysis, in: SIAM J. Control Optim., 2008, vol. 47, n^o 2, pp. 817–848. [ DOI : 10.1137/060655286 ]
  http://www.arxiv.org/abs/math.OC/0603619
• 63M. Akian, S. Gaubert, M. Sharify.
  Log-majorization of the moduli of the eigenvalues of a matrix polynomial by tropical roots, 2013, Preprint arXiv:1304.2967, 29 pages, 5 figures.
  http://hal.inria.fr/hal-00881196
• 64M. Akian, S. Gaubert, C. Walsh.
  The max-plus Martin boundary, in: Doc. Math., 2009, vol. 14, pp. 195–240.
  http://arxiv.org/abs/math/0412408
• 65M. Akian, J.-P. Quadrat, M. Viot.
  Duality between probability and optimization, in: Idempotency, J. Gunawardena (editor), Publications of the Isaac Newton Institute, Cambridge University Press, 1998.
• 66X. Allamigeon.
  On the Complexity of Strongly Connected Components in Directed Hypergraphs, in: Algorithmica, January 2013, Published on line. [ DOI : 10.1007/s00453-012-9729-0 ]
  http://hal.inria.fr/hal-00782846
• 67X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the simplex algorithm, in: ILAS 2013 - 18th Conference of the International Linear Algebra Society, Providence, RI, United States, June 2013.
  http://hal.inria.fr/hal-00930959
• 68X. Allamigeon, P. Benchimol, S. Gaubert, M. Joswig.
  Tropicalizing the Simplex Algorithm, in: SMAI 2013 - 6ème biennale des mathématiques appliquées et industrielles, Seignosse, France, May 2013, Poster présentant l'article arXiv:1308.0454.
  http://hal.inria.fr/hal-00930941
• 69X. Allamigeon, U. Fahrenberg, S. Gaubert, R. D. Katz, A. Legay.
  Tropical Fourier-Motzkin elimination, with an application to real-time verification, 2013, Preprint arXiv:1308.2122.
  http://hal.inria.fr/hal-00935072
• 70X. Allamigeon, S. Gaubert, E. Goubault.
  Inferring Min and Max Invariants Using Max-plus Polyhedra, in: Proceedings of the 15th International Static Analysis Symposium (SAS'08), Springer, 2008, vol. 5079, Valencia, Spain, 16-18 July 2008.
• 71X. Allamigeon, S. Gaubert, E. Goubault.
  The tropical double description method, in: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science (STACS'2010), Nancy, France, March 4-6 2010.
  http://drops.dagstuhl.de/opus/volltexte/2010/2443/pdf/1001.AllamigeonXavier.2443.pdf
• 72X. Allamigeon, S. Gaubert, E. Goubault.
  Computing the Vertices of Tropical Polyhedra using Directed Hypergraphs, in: Discrete and Computational Geometry, February 2013, vol. 49, n^o 2, pp. 247-279. [ DOI : 10.1007/s00454-012-9469-6 ]
  http://hal.inria.fr/hal-00782862
• 73X. Allamigeon, S. Gaubert, V. Magron, B. Werner.
  Certification of Bounds of Non-linear Functions: the Templates Method, in: Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, United Kingdom, J. Carette, D. Aspinall, C. Lange, P. Sojka, W. Windsteige (editors), Lecture Notes in Computer Science, Springer Berlin Heidelberg, July 2013, vol. 7961, pp. 51-65. [ DOI : 10.1007/978-3-642-39320-4_4 ]
  http://hal.inria.fr/hal-00932333
• 74X. Allamigeon, S. Gaubert, V. Magron, B. Werner.
  Certification of inequalities involving transcendental functions: combining SDP and max-plus approximation, in: European Control Conference (ECC'13), Zurich, Switzerland, 2013, pp. 2244 - 2250.
  http://hal.inria.fr/hal-00932348
• 75X. Allamigeon, R. Katz.
  Minimal external representations of tropical polyhedra, in: Journal of Combinatorial Theory, Series A, 2013, vol. 120, n^o 4, pp. 907-940. [ DOI : 10.1016/j.jcta.2013.01.011 ]
  http://hal.inria.fr/hal-00782837
• 76N. Bacaër.
  Perturbations singulières et théorie spectrale min-plus, Université Paris 6, January 2002.
• 77F. Baccelli, D. Hong.
  TCP is max-plus linear and what it tells us on its throughput, in: Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2000, pp. 219-230.
• 78R. Bapat.
  A max version of the Perron-Frobenius theorem, in: Linear Algebra Appl., 1998, vol. 275/276, pp. 3–18.
• 79R. Bapat, T. Raghavan.
  Nonnegative matrices and applications, Cambridge university press, 1997, n^o 64, XIII+336 p.
• 80R. J. Bayardo, B. Panda.
  Fast Algorithms for Finding Extremal Sets, in: Proceedings of the SIAM International Conference on Data Mining, SDM 2011, SIAM, 2011.
• 81A. Benveniste, S. Gaubert, C. Jard.
  Monotone rational series and max-plus algebraic models of real-time systems, in: Proc. of the Fourth Workshop on Discrete Event Systems (WODES98), Cagliari, Italy, IEE, 1998.
• 82A. Berenstein, A. N. Kirillov.
  The Robinson-Schensted-Knuth bijection, quantum matrices, and piece-wise linear combinatorics, in: Proceedings of FPSAC'01, 2001.
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  Exponential behaviour of the Butkovič-Zimmermann algorithm for solving two-sided linear systems in max-algebra, in: Discrete Appl. Math., 2008, vol. 156, n^o 18, pp. 3506–3509.
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• 84T. Blyth, M. Janowitz.
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  Algorithmes d'itération sur les politiques pour les applications monotones contractantes, École des Mines, Dec. 2001.
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• 96J. Cochet-Terrasson, G. Cohen, S. Gaubert, M. Mc Gettrick, J.-P. Quadrat.
  Numerical computation of spectral elements in max-plus algebra, in: Proc. of the IFAC Conference on System Structure and Control, Nantes, July 1998.
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• 98J.-P. Comet.
  Application of max-plus algebra to biological sequence comparison, in: Theor. Comput. Sci., Special issue on max-plus algebras, 2003, vol. 293, pp. 189–217.
• 99A. Costan, S. Gaubert, E. Goubault, M. Martel, S. Putot.
  A policy iteration algorithm for computing fixed points in static analysis of programs, in: Proceedings of the 17th International Conference on Computer Aided Verification (CAV'05), Edinburgh, LNCS, Springer, July 2005, pp. 462–475.
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  Comparison of the Galois connection and widening/narrowing approaches to abstract interpretation. JTASPEFL$$'91, Bordeaux, in: BIGRE, October 1991, vol. 74, pp. 107–110.
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