Setting 2 variables at a time yields a new lower bound for random 3-sat, Proceeding of the 32nd ACM Symposium on Theory of ComputingAch01] Dimitris Achlioptas. Lower bounds for random 3-sat via dierential equations, p.2837, 2000. ,
Two applications of urn processes the fringe analysis of search trees and the simulation of quasi-stationnary distributions of markov-chains, Probability in the engineering and informational sciences, p.293307, 1988. ,
Embedding of Urn Schemes into Continuous Time Markov Branching Processes and Related Limit Theorems, The Annals of Mathematical Statistics, vol.39, issue.6, p.18011817, 1968. ,
DOI : 10.1214/aoms/1177698013
Branching processes, 2004. ,
DOI : 10.1007/978-3-642-65371-1
Optimal myopic algorithms for random 3-sat, Annual Symposium on Foundations of Computer Science, p.590600, 2000. ,
The scaling window of the 2-SAT transition. Random Structures Algorithms, p.201256, 2001. ,
Phase transition and nite-size scaling for the integer partitioning problem, Random Structures Algorithms Analysis of algorithms, vol.19, issue.3- 4, p.247288, 2000. ,
Random maps, coalescing saddles, singularity analysis, and Airy phenomena Analysis of algorithms, Random Structures Algorithms, vol.19, issue.3-4, 2000. ,
On the satisability and maximum satisability of random 3-CNF formulas, Proceedings of the Fourth Annual ACM- SIAM Symposium on Discrete Algorithms, p.322330, 1993. ,
Probability and measure Wiley Series in Probability and Mathematical Statistics : Probability and Mathematical Statistics, 1986. ,
Asymptotic Normality in the Generalized Polya???Eggenberger Urn Model, with an Application to Computer Data Structures, SIAM Journal on Algebraic Discrete Methods, vol.6, issue.3, p.394405, 1985. ,
DOI : 10.1137/0606041
Calcul diérentiel, 1967. ,
Probabilistic analysis of two heuristics for the 3- satisability problem, SIAM Journal on Computing, vol.15, issue.4, p.11061118, 1986. ,
Probabilistic analysis of a generalization of the unitclause literal selection heuristics for the k-satisability problem, Information Sciences. An International Journal, vol.51, issue.3, p.289314, 1990. ,
Advanced combinatorics The art of nite and innite expansions, 1974. ,
The complexity of theorem proving procedures, Third annual ACM symposium on theory of computing, p.151158, 1971. ,
Mick gets some (the odds are on his side), 33rd Annual Symposium on Foundations of Computer Science, p.620627, 1992. ,
Many hard examples for resolution, Journal of the ACM, vol.35, issue.4, p.759768, 1988. ,
DOI : 10.1145/48014.48016
Asymptotic methods in analysis, 1981. ,
A general upper bound for the satisability threshold of random r-SAT formulae, Journal of Algorithms, vol.24, issue.2, p.395420, 1997. ,
Length of prime implicants and number of solutions of random CNF formulae A unied presentation of some urn models Average-case analysis of algorithms, Theoret. Comput. Sci. Algorithmica, vol.215, issue.2912, p.130120147, 1998. ,
The 3-xorsat threshold, C. R. Math. Acad. Sci. Paris, vol.335, issue.11, p.963966, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-01185801
Typical 3-sat formulae and the satisability threshold, Electronic Colloquium on computational complexity, 2003. ,
A computing procedure for quantication theory, Journal of the association for computing machinery, vol.7, p.201215, 1960. ,
Upper bounds on the satisability threshold, Phase transitions in combinatorial problems, p.187197, 1999. ,
Combinatoire analytique et algorithmique des ensembles de données, Thèse de doctorat, École polytechnique, 2004. ,
Über zwei bekannte Einwände gegen das Boltzmannsche h-Theorem, Physik, Zs, vol.8, p.311314, 1907. ,
On random 3-sat, Combinatorics, Probability and Computing, vol.4, issue.3, p.189195, 1995. ,
Über die Statistik verketteter Vorgänge. Zeitschrift für angewandte mathematik und mechanik, p.279289, 1923. ,
On random graphs. I. Publ, Math. Debrecen, vol.6, p.290297, 1959. ,
On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl, vol.5, p.1761, 1960. ,
An introduction to probability theory and its applications ,
On Ramanujan's Q-function, Journal of Computational and Applied Mathematics, vol.58, issue.1, p.103116, 1995. ,
DOI : 10.1016/0377-0427(93)E0258-N
Analytic urns, The Annals of Probability, vol.33, issue.3, 2004. ,
DOI : 10.1214/009117905000000026
Singularity analysis of generating functions ,
URL : https://hal.archives-ouvertes.fr/inria-00075725
Probabilistic analysis of the Davis-Putnam procedure for solving the satisability problem, FP05a] Philippe Flajolet et Vincent Puyhaubert. Analytic combinatorics at Ok Corral, p.7787, 1983. ,
Triangular urns of dimension 2 and 3 ,
Results related to threshold phenomena research in satisability : lower bounds, Phase transitions in combinatorial problems, p.147157, 1999. ,
Bernard Friedman's urn, Ann. Math. Statist, vol.36, p.956970, 1965. ,
A simple urn model, Communications on Pure and Applied Mathematics, vol.27, issue.1, p.5970, 1949. ,
DOI : 10.1002/cpa.3160020103
Sharp thresholds of graph properties, and the k-sat problem, J ,
Analytic combinatorics. A paraître Une version préliminaire des 9 premiers chapitres est disponible sur le web à l'adresse http ,
DOI : 10.1017/cbo9780511801655
URL : https://hal.archives-ouvertes.fr/inria-00072739
Analysis of Two Simple Heuristics on a Random Instance ofk-sat, Journal of Algorithms, vol.20, issue.2, p.312355, 1996. ,
DOI : 10.1006/jagm.1996.0016
A guide to the theory of NP-completeness, Series of Books in the Mathematical Sciences, 1979. ,
Martingale Functional Central Limit Theorems for a Generalized Polya Urn, The Annals of Probability, vol.21, issue.3, p.16241639, 1993. ,
DOI : 10.1214/aop/1176989134
Théorèmes limites pour les structures combinatoires et les fonctions arithmétiques, Thèse de doctorat, École polytechnique, 1994. ,
On Convergence Rates in the Central Limit Theorems for Combinatorial Structures, European Journal of Combinatorics, vol.19, issue.3, p.329343, 1998. ,
DOI : 10.1006/eujc.1997.0179
Functional limit theorems for multitype branching processes and generalized Pólya urns. Stochastic Process, Appl, vol.110, issue.2, p.177245, 2004. ,
Limit theorems for triangular urn schemes, Probability Theory and Related Fields, vol.65, issue.3, 2005. ,
DOI : 10.1007/s00440-005-0442-7
Urn models and their application An approach to modern discrete probability theory, 1977. ,
The birth of the giant component. Random Structures Algorithms, p.231358, 1993. ,
Bounding the unsatisability threshold of random 3-SAT. Random Structures Algorithms, p.103116, 2000. ,
Martingales in the Ok Corral, Bulletin of the London Mathematical Society, vol.31, issue.5, pp.601-606, 1999. ,
DOI : 10.1112/S0024609399006098
Approximating the unsatisability threshold of random formulas. Random Structures and Algorithms, p.253269, 1998. ,
The probabilistic analysis of a greedy satisability algorithm, Lecture Notes in Computer Science, vol.2461, p.574585, 2002. ,
Coupon collectors, q-binomial coecients and the unsatisability threshold, 7th Italian Conference, volume 2202 de Lecture Notes in Computer Science, p.328338, 2001. ,
Tail bounds for occupancy and the satisability threshold conjecture. Random Structures and Algorithms, p.5980, 1995. ,
On generalized P??lya urn models, Statistics & Probability Letters, vol.49, issue.2, p.163173, 2000. ,
DOI : 10.1016/S0167-7152(00)00045-6
The art of computer programming Seminumerical Algorithms, 1969. ,
The art of computer programming ,
Solution to the OK Corral model via decoupling of Friedman's urn, J. Theoret. Probab, vol.16, issue.1, p.267276, 2003. ,
Pólya urn models and connections to random trees : A review, 2005. ,
Étude des transitions de phases en K-satisfaisabilité, 2000. ,
Statistical mechanics methods and phase transitions in optimization problems, Phase transitions in combinatorial problems, p.367, 1999. ,
An integral representation for Eulerian numbers. Dans Sets, graphs and numbers (Budapest, 1991), volume 60 de Colloq, Math. Soc. János Bolyai, p.513527, 1992. ,
Sur quelques points de la théorie des probabilités, Annales Institut Poincaré, vol.1, p.118161, 1931. ,
An analytic approach for the analysis of rotations in fringe-balanced binary search trees, Annals of Combinatorics, vol.19, issue.2, p.173184, 1998. ,
DOI : 10.1007/BF01608487
Generating functions and the satisability threshold, Discrete Mathematics and Theoretical Computer Science, vol.6, issue.2, p.425436, 2004. ,
étude statistique de l'existence de solutions de problèmes sat, application aux systèmes-experts, p.283286, 1986. ,
The complexity of satisability problems, Conference Record of the Tenth Annual ACM Symposium on theory of computing, p.216226 ,
Central limit theorems for urn models. Stochastic Process, Appl, vol.65, issue.1, p.115137, 1996. ,
de Cambridge Studies in Advanced Mathematics, Enumerative combinatorics, vol.1, issue.49, 1997. ,
On the method of saddle points, Applied Scientific Research, Section B, vol.67, issue.1, p.3345, 1951. ,
DOI : 10.1007/BF02919754
The Ok Corral and the Power of the Law (A Curious Poisson-Kernel Formula for a Parabolic Equation), Bulletin of the London Mathematical Society, vol.30, issue.2, p.166170, 1998. ,
DOI : 10.1112/S0024609397004062
On random 2?3 trees, Acta Informatica, vol.1, issue.2, p.15917078, 1977. ,
DOI : 10.1007/BF00289075