BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
An Improved Bound for Joints in Arrangements of Lines in Space
Discrete & Computational Geometry
An Improved Analysis of Linear Mergers
Computational Complexity
Kakeya Sets, New Mergers and Old Extractors
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Improved decoding of Reed-Solomon and algebraic-geometry codes
IEEE Transactions on Information Theory
Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy
IEEE Transactions on Information Theory
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The finite field Kakeya problem deals with the way lines in different directions can overlap in a vector space over a finite field. This problem came up in the study of certain Euclidean problems and, independently, in the search for explicit randomness extractors. We survey recent progress on this problem and describe several of its applications.