Resource bounded symmetry of information revisited
Theoretical Computer Science - Mathematical foundations of computer science 2004
Variations on Muchnik's Conditional Complexity Theorem
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Reconstructive dispersers and hitting set generators
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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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 l\log \left\| {A^{ = n} } \right\| 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 0((\sqrt {\log \left\| {A^{ = n} } \right\|}+ \log n)\log n); using both nondeterminism and randomness, we can make do with an excess term of 0(\log ^3 n). With randomness alone, we show a lower bound of n - \log \left\| {A^{ = n} } \right\| - 0(\log n) on the description length of strings in A of length n, and a lower bound of 2 \cdot \log \left\| {A^{ = n} } \right\| - 0(1) on the length of any program that distinguishes a given string length n in A from any other string. The latter lower bound is tight up to an additive term of 0(log n).The key ingredient for our upperbounds is the relativizable hardness versus randomness trade offs based on the Nisan-Wigderson pseudorandom generator construction.