
Automating Resolution is NPHard
We show that the problem of finding a Resolution refutation that is at m...
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On the Complexity of Branching Proofs
We consider the task of proving integer infeasibility of a bounded conve...
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Complexity of cutting planes and branchandbound in mixedinteger optimization
We investigate the theoretical complexity of branchandbound (BB) and c...
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Optimally cutting a surface into a disk
We consider the problem of cutting a set of edges on a polyhedral manifo...
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A RoundCollapse Theorem for ComputationallySound Protocols; or, TFNP is Hard (on Average) in Pessiland
Consider the following two fundamental open problems in complexity theor...
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Pivot Rules for CircuitAugmentation Algorithms in Linear Optimization
Circuitaugmentation algorithms are a generalization of the Simplex meth...
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How incomputable is Kolmogorov complexity?
Kolmogorov complexity is the length of the ultimately compressed version...
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Automating Cutting Planes is NPHard
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, 1) It is NPhard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and 2)unless GapHittingSet admits a nontrivial algorithm, one cannot find a treelike CP refutation of F in time polynomial in the length of the shortest such refutation. The first result extends the recent breakthrough of Atserias and Müller (FOCS 2019) that established an analogous result for Resolution. Our proofs rely on two new lifting theorems: (1) Daglike lifting for gadgets with many output bits. (2) Treelike lifting that simulates an rround protocol with gadgets of query complexity O(log r) independent of input length.
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