Proving Unsatisfiability of CNFs Locally
Journal of Automated Reasoning
Homogenization and the Polynominal Calculus
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
ISAAC '99 Proceedings of the 10th International Symposium on Algorithms and Computation
A Study of Proof Search Algorithms for Resolution and Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Transformation rules for CNOT-based quantum circuits and their applications
New Generation Computing - Quantum computing
Homogenization and the polynomial calculus
Computational Complexity
Solving #SAT and Bayesian inference with backtracking search
Journal of Artificial Intelligence Research
Value elimination: bayesian inference via backtracking search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Tight bounds for monotone switching networks via fourier analysis
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We prove an exponential lower bound for tree-like Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between tree-like and dag-like proofs for both Cutting Planes and resolution; in both cases only superpolynomial separations were known before. In order to prove this, we extend the lower bounds on the depth of monotone circuits of Raz and McKenzie (FOCS 1997) to monotone real circuits.In the case of resolution, we further improve this result by giving an exponential separation of tree-like resolution from (dag-like) regular resolution proofs. In fact, the refutation provided to give the upper bound respects the stronger restriction of being a Davis-Putnam resolution proof. This extends the corresponding superpolynomial separation of Urquhart (Bull. Symb. Logic 1, 1995).Finally, we prove an exponential separation between Davis-Putnam resolution and unrestricted resolution proofs; only a superpolynomial separation was previously known from Goerdt (Ann. Math. Artificial Intelligence 6, 1992).