Addressing a question of Gowers, we determine the order of the tower height for the partition size in a version of Szemerédi’s regularity lemma.

We provide efficient algorithms for learning disjunctions in the semi-supervised setting under a natural regularity assumption introduced by (Balcan & Blum, 2005). We prove bounds on the sample complexity of our algorithms under a mild restriction on the data distribution. We also give an active learning algorithm with improved sample complexity and extend all our algorithms to the random class...

We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite λ-terms that are λletrec-expressible in the sense that they arise as infinite unfoldings of terms in λletrec, the λ-calculus with letrec. We provide two characterizations, using concepts we introduce for infinite λ-terms: regularity, strong regularity, ...

We prove a version of Szemerédi’s regularity lemma for subsets of a typical random set in F p . As an application, a result on the distribution of three-term arithmetic progressions in sparse sets is discussed.

Chvátal, Rödl, Szemerédi and Trotter [1] proved that the Ramsey numbers of graphs of bounded maximum degree are linear in their order. We prove that the same holds for 3-uniform hypergraphs. The main new tool which we prove and use is an embedding lemma for 3-uniform hypergraphs of bounded maximum degree into suitable 3-uniform ‘pseudo-random’ hypergraphs. keywords: hypergraphs; regularity lemm...