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156
A variant of the hypergraph removal lemma
, 2006
"... Abstract. Recent work of Gowers [10] and Nagle, Rödl, Schacht, and Skokan [15], [19], [20] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [26] and FurstenbergKatznelson [7] concerning onedimensional and multidimensional arithmetic progressions respecti ..."
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Cited by 75 (7 self)
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Abstract. Recent work of Gowers [10] and Nagle, Rödl, Schacht, and Skokan [15], [19], [20] has established a hypergraph removal lemma, which in turn implies some results of Szemerédi [26] and FurstenbergKatznelson [7] concerning onedimensional and multidimensional arithmetic progressions
Transaction Lemmas
"... Writing and reasoning about concurrent programs remains notoriously difficult despite the proliferation of type systems, static analyses, and dynamic analyses targeting concurrent programs. There are examples of verified developments for concurrent languages and programs (Chou and Peled 1996; Affeld ..."
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of wellknown facts about relations and program traces, we prove that Velodrome accurately reconstructs the transactional happensbefore relation, the quotient of the usual happensbefore relation where operations in the same transaction are identified. Although this proof is still a work in progress, we
Szemerédi’s regularity lemma for sparse graphs
 Foundations of Computational Mathematics
, 1997
"... A remarkable lemma of Szemeredi asserts that, very roughly speaking, any dense graph can be decomposed into a bounded number of pseudorandom bipartite graphs. This farreaching result has proved to play a central r^ole in many areas of combinatorics, both `pure ' and `algorithmic. ' The ..."
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Cited by 68 (18 self)
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; The quest for an equally powerful variant of this lemma for sparse graphs has not yet been successful, but some progress has been achieved recently. The aim of this note is to report on the successes so far.
On the Bogolyubov–Ruzsa lemma
, 2012
"... Our main result is that if A is a finite subset of an abelian group with jACAj 6 KjAj, then 2A 2A contains an O.logO.1 / 2K/dimensional coset progression M of size at least exp.O.logO.1 / 2K//jAj. ..."
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Cited by 11 (1 self)
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Our main result is that if A is a finite subset of an abelian group with jACAj 6 KjAj, then 2A 2A contains an O.logO.1 / 2K/dimensional coset progression M of size at least exp.O.logO.1 / 2K//jAj.
THE SYMMETRY PRESERVING REMOVAL LEMMA
, 2009
"... In this paper we observe that in the hypergraph removal lemma, the edge removal can be done in such a way that the symmetries of the original hypergraph remain preserved. As an application we prove the following generalization of Szemerédi’s Theorem on arithmetic progressions. Let A be an Abelian g ..."
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Cited by 4 (0 self)
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In this paper we observe that in the hypergraph removal lemma, the edge removal can be done in such a way that the symmetries of the original hypergraph remain preserved. As an application we prove the following generalization of Szemerédi’s Theorem on arithmetic progressions. Let A be an Abelian
Szemerédi’s regularity lemma revisited
 Contrib. Discrete Math
"... Abstract. Szemerédi’s regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi’s theorem on arithmetic progressions [19], [18]. In this note we revisit this lemma from the perspective of probability theory and inf ..."
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Cited by 25 (3 self)
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Abstract. Szemerédi’s regularity lemma is a basic tool in graph theory, and also plays an important role in additive combinatorics, most notably in proving Szemerédi’s theorem on arithmetic progressions [19], [18]. In this note we revisit this lemma from the perspective of probability theory
Improving the First Selection Lemma in R³
, 2010
"... We present new bounds on the first selection lemma in R 3. This makes progress on the open problems of Bukh, Matoušek and Nivash [BMN08] and BorosFüredi [BF84] for the threedimensional case, improving the previously best result of Wagner [Wag03]. While our results narrow the gap between the curren ..."
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Cited by 1 (0 self)
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We present new bounds on the first selection lemma in R 3. This makes progress on the open problems of Bukh, Matoušek and Nivash [BMN08] and BorosFüredi [BF84] for the threedimensional case, improving the previously best result of Wagner [Wag03]. While our results narrow the gap between
ON THE TRIANGLE REMOVAL LEMMA FOR SUBGRAPHS OF SPARSE PSEUDORANDOM GRAPHS
, 2010
"... We study an extension of the triangle removal lemma of Ruzsa and Szemerédi [Triple systems with no six points carrying three triangles, Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, NorthHolland, Amsterdam, 1978, pp. 939–945], which gave rise to a purely combinatorial pr ..."
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Cited by 4 (1 self)
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proof of the fact that sets of integers of positive upper density contain threeterm arithmetic progressions, a result first proved by Roth [On certain sets of integers, J. London Math. Soc. 28 (1953), 104–109]. We obtain a generalization of the triangle removal lemma for subgraphs of sparse
New Algorithmic Aspects Of The Local Lemma With Applications To Routing And Partitioning
"... . The Lov'asz Local Lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy & Reed) have led to constructive versions. However, these metho ..."
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Cited by 31 (6 self)
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. The Lov'asz Local Lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy & Reed) have led to constructive versions. However
Dynamic Rippling, MiddleOut Reasoning and Lemma Discovery
"... Abstract. We present a succinct account of dynamic rippling, a technique used to guide the automation of inductive proofs. This simplifies termination proofs for rippling and hence facilitates extending the technique in ways that preserve termination. We illustrate this by extending rippling with a ..."
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Cited by 1 (1 self)
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terminating version of middleout reasoning for lemma speculation. This supports automatic speculation of schematic lemmas which are incrementally instantiated by unification as the rippling proof progresses. Middleout reasoning and lemma speculation have been implemented in higherorder logic and evaluated
Results 1  10
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156