Many hard examples for resolution
Journal of the ACM (JACM)
A randomised 3-colouring algorithm
Discrete Mathematics - Graph colouring and variations
A spectral technique for coloring random 3-colorable graphs (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A threshold for unsatisfiability
Journal of Computer and System Sciences
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
An improved upper bound on the non-3-colourability threshold
Information Processing Letters
Approximating the unsatisfiability threshold of random formulas
Random Structures & Algorithms
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximating the Independence Number and the Chromatic Number in Expected Polynominal Time
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The analysis of a list-coloring algorithm on a random graph
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Simplified and improved resolution lower bounds
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Short Propositional Refutations for Dense Random 3CNF Formulas
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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It is known that random k-SAT instances with at least cn clauses where c = ck is a suitable constant are unsatisfiable (with high probability). We consider the problem to certify efficiently the unsatisfiability of such formulas. A result of Beame et al. shows that k-SAT instances with at least nk-1/ log n clauses can be certified unsatisfiable in polynomial time. We employ spectral methods to improve on this: We present a polynomial time algorithm which certifies random k-SAT instances for k even with at least 2k ċ (k/2)7 ċ (ln n)7 ċ nk/2 = n(k/2)+o(1) clauses as unsatisfiable (with high probability).