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46
Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems
, 1998
"... We prove an exponential lower bound for treelike Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between treelike and daglike proofs for both CuttingPlanes and resolution; in both cases only superpolynomial se ..."
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Cited by 24 (5 self)
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We prove an exponential lower bound for treelike Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential separation between treelike and daglike proofs for both CuttingPlanes and resolution; in both cases only superpolynomial
On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems
, 2000
"... An exponential lower bound for the size of treelike Cutting Planes refutations of a certain family of CNF formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the treelike versions and the daglike versions of resolution and Cutting Planes. ..."
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Cited by 37 (6 self)
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An exponential lower bound for the size of treelike Cutting Planes refutations of a certain family of CNF formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the treelike versions and the daglike versions of resolution and Cutting Planes
Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic
"... A proof of the (propositional) Craig interpolation theorem for cutfree sequent calculus yields that a sequent with a cutfree proof (or with a proof with cutformulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuitsize is at most k. We ..."
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Cited by 93 (4 self)
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corresponding to the bounded arithmetic theory S 2 2 (ff). (c) linear equational calculus. (d) cutting planes. 2. New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]). (b) for the cutting planes proof system with coefficients written in unary ([4]). 3. An alternative proof
The Space Complexity of Cutting Planes Refutations
 In Proceedings of the 30th Annual Computational Complexity Conference (CCC ’15) (Leibniz International Proceedings in Informatics (LIPIcs
, 2015
"... Abstract We study the space complexity of the cutting planes proof system, in which the lines in a proof are integral linear inequalities. We measure the space used by a refutation as the number of linear inequalities that need to be kept on a blackboard while verifying it. We show that any unsatis ..."
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Cited by 3 (1 self)
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restriction of cutting planes, in which all coefficients have size bounded by a constant. We show that there is a CNF which requires superconstant space to refute in this system. The system nevertheless already has an exponential speedup over resolution with respect to size, and we additionally show
On the Complexity of Propositional Proof Systems
, 2000
"... In the thesis we have investigated the complexity of proofs in several propositional proof systems. Our main motivation has been to contribute to the line of research started by Cook and Reckhow to obtain how much knowledge as possible about the complexity of different proof systems to show that the ..."
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Cited by 1 (0 self)
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in several proof systems (resolution and some of its restrictions, Cutting Planes, Polynomial Calculus, Frege systems). Our results give better or new separations between such proof systems. On the other hand our work also concerns with automated theorem proving questions in resolution and Polynomial
Complexity of Semialgebraic Proofs with Restricted Degree of Falsity
, 2008
"... The degree of falsity of an inequality in Boolean variables shows how many variables are enough to substitute in order to satisfy the inequality. Goerdt introduced a weakened version of the Cutting Plane (CP) proof system with a restriction on the degree of falsity of intermediate inequalities [6]. ..."
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The degree of falsity of an inequality in Boolean variables shows how many variables are enough to substitute in order to satisfy the inequality. Goerdt introduced a weakened version of the Cutting Plane (CP) proof system with a restriction on the degree of falsity of intermediate inequalities [6
Search Space and Average Proof Length of Resolution
, 1993
"... In this paper we introduce a definition of search trees for resolution based proof procedures. This definition describes more clearly the differences between the restrictions of resolution. Applying this concept to monotone restrictions of the resolution it is shown that the average proof length for ..."
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systems like cutting plane systems, DavisPutnam algorithms etc. with respect to the minimal proof length, e.g. see [6]. Also restrictions of the resolution proof procedure can be classified in this way [2], [3], [4], [5], [9], [10]. But these papers deal with worstcase complexities. In practice many
Exponential lower bounds and Integrality Gaps for Treelike LovászSchrijver Procedures
, 2007
"... The matrix cuts of Lovász and Schrijver are methods for tightening linear relaxations of zeroone programs by the addition of new linear inequalities. We address the question of how many new inequalities are necessary to approximate certain combinatorial problems with strong guarantees, and to solve ..."
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Cited by 10 (1 self)
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that treelike LS+ cannot polynomially simulate treelike cutting planes, and that treelike LS+ cannot polynomially simulate unrestricted resolution. All of our size lower bounds for derivation trees are based upon connections between the size and height of the derivation tree (its rank). The primary
Improved lower bounds for treelike resolution over linear inequalities
 In In Proceedings of the 10th International Conference on Theory and Applications of Satisfiability Testing (SAT), 2007. Preliminary version in Electronic Colloquium on Computational Complexity, ECCC
, 2007
"... Abstract. We continue a study initiated by Krajíček of a Resolutionlike proof system working with clauses of linear inequalities, R(CP). For all proof systems of this kind Krajíček proved in [1] an exponential lower bound of the form: exp(n Ω(1)) M O(W log2 n) where M is the maximal absolute value o ..."
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Cited by 1 (0 self)
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Abstract. We continue a study initiated by Krajíček of a Resolutionlike proof system working with clauses of linear inequalities, R(CP). For all proof systems of this kind Krajíček proved in [1] an exponential lower bound of the form: exp(n Ω(1)) M O(W log2 n) where M is the maximal absolute value
unknown title
"... We present the experimental reconstruction of subwavelength features from the farfield of sparse optical objects. We show that it is sufficient to know that the object is sparse, and only that, and recover 100 nm features with the resolution of 30 nm, for an illuminating wavelength of =532 nm. Our ..."
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We present the experimental reconstruction of subwavelength features from the farfield of sparse optical objects. We show that it is sufficient to know that the object is sparse, and only that, and recover 100 nm features with the resolution of 30 nm, for an illuminating wavelength of =532 nm
Results 1  10
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46