Results 1 - 10 of 156

A variant of the hypergraph removal lemma

by Terence Tao , 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 Furstenberg-Katznelson [7] concerning one-dimensional and multi-dimensional arithmetic progressions respecti ..."
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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 Furstenberg-Katznelson [7] concerning one-dimensional and multi-dimensional arithmetic progressions

Transaction Lemmas

by Caitlin Sadowski, Jaeheon Yi, Kenneth Knowles, Cormac Flanagan
"... 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 well-known facts about relations and program traces, we prove that Velodrome accurately reconstructs the transactional happens-before relation, the quotient of the usual happens-before 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

by Y. Kohayakawa - 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 far-reaching result has proved to play a central r^ole in many areas of combinatorics, both `pure ' and `algorithmic. ' The ..."
Abstract - Cited by 68 (18 self) - Add to MetaCart
; 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

by Tom Sanders , 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. ..."
Abstract - Cited by 11 (1 self) - Add to MetaCart
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

by BALÁZS SZEGEDY , 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 ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
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

by Terence Tao - 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 ..."
Abstract - Cited by 25 (3 self) - Add to MetaCart
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

by Abdul Basit, Nabil H. Mustafa, Sarfraz Raza, Saurabh Ray , 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 Boros-Füredi [BF84] for the three-dimensional case, improving the previously best result of Wagner [Wag03]. While our results narrow the gap between the curren ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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 Boros-Füredi [BF84] for the three-dimensional 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

by Yoshiharu Kohayakawa, Vojtěch Rödl, Mathias Schacht, Jozef Skokan , 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, North-Holland, Amsterdam, 1978, pp. 939–945], which gave rise to a purely combinatorial pr ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
proof of the fact that sets of integers of positive upper density contain three-term 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

by Tom Leighton, Chi-Jen Lu, SATISH RAO, ARAVIND SRINIVASAN
"... . 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 ..."
Abstract - Cited by 31 (6 self) - Add to MetaCart
. 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, Middle-Out Reasoning and Lemma Discovery

by Moa Johansson, Lucas Dixon, Alan Bundy
"... 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 ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
terminating version of middle-out reasoning for lemma speculation. This supports automatic speculation of schematic lemmas which are incrementally instantiated by unification as the rippling proof progresses. Middle-out reasoning and lemma speculation have been implemented in higher-order logic and evaluated
Results 1 - 10 of 156