Many hard examples for resolution
Journal of the ACM (JACM)
Lower bounds for random 3-SAT via differential equations
Theoretical Computer Science - Phase transitions in combinatorial problems
Optimal myopic algorithms for random 3-SAT
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A sharp threshold in proof complexity yields lower bounds for satisfiability search
Journal of Computer and System Sciences - STOC 2001
Threshold values of random K-SAT from the cavity method
Random Structures & Algorithms
The probabilistic analysis of a greedy satisfiability algorithm
Random Structures & Algorithms
Algorithmic Barriers from Phase Transitions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On the satisfiability threshold of formulas with three literals per clause
Theoretical Computer Science
Information, Physics, and Computation
Information, Physics, and Computation
Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Proceedings of the forty-second ACM symposium on Theory of computing
On belief propagation guided decimation for random k-SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Tight bounds for LDPC and LDGM codes under MAP decoding
IEEE Transactions on Information Theory
Exponential lower bounds for DPLL algorithms on satisfiable random 3-CNF formulas
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Going after the k-SAT threshold
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The interpolation method, originally developed in statistical physics, transforms distributions of random CSPs to distributions of much simpler problems while bounding the change in a number of associated statistical quantities along the transformation path. After a number of further mathematical developments, it is now known that, in principle, the method can yield rigorous unsatisfiability bounds if one "plugs in an appropriate functional distribution". A drawback of the method is that identifying appropriate distributions and plugging them in leads to major analytical challenges as the distributions required are, in fact, infinite dimensional objects. We develop a variant of the interpolation method for random CSPs on arbitrary sparse degree distributions which trades accuracy for tractability. In particular, our bounds only require the solution of a 1-dimensional optimization problem (which typically turns out to be very easy) and as such can be used to compute explicit rigorous unsatisfiability bounds.