Random-self-reducibility of complete sets
SIAM Journal on Computing
Journal of Computer and System Sciences
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Decoding of Reed Solomon codes beyond the error-correction bound
Journal of Complexity
Two-Tape Simulation of Multitape Turing Machines
Journal of the ACM (JACM)
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Resource-Bounded Kolmogorov Complexity Revisited
SIAM Journal on Computing
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Proofs, Codes, and Polynomial-Time Reducibilities
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
New Bounds for the Language Compression Problem
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Extractors from Reed-Muller Codes
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Compression of samplable sources
Computational Complexity
On the optimal compression of sets in PSPACE
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
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The language compression problem asks for succinct descriptions of the strings in a language A such that the strings can be efficiently recovered from their description when given a membership oracle for A. We study randomized and nondeterministic decompression schemes and investigate how close we can get to the information theoretic lower bound of log ||A=n|| for the description length of strings of length n.Using nondeterminism alone, we can achieve the information theoretic lower bound up to an additive term of O((√log ||A=n|| + log n) log n); using both nondeterminism and randomness, we can make do with an excess term of O (log3 n). With randomness alone, we show a lower bound of n - log ||A=n|| - O(log n) on the description length of strings in A of length n, and a lower bound of 2 ċ log ||A=n|| - O(1) on the length of any program that distinguishes a given string of length n in A from any other string. The latter lower bound is tight up to an additive term of O(log n).The key ingredient for our upper bounds is the relativizable hardness versus randomness tradeoffs based on the Nisan-Wigderson pseudorandora generator construction.