NP is as easy as detecting unique solutions
Theoretical Computer Science
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Symmetry of information and one-way functions
Information Processing Letters
Journal of Computer and System Sciences
On symmetry of information and polynomial time invertibility
Information and Computation
On resource-bounded instance complexity
Theoretical Computer Science
Two heads are better than two tapes
Journal of the ACM (JACM)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
NP might not be as easy as detecting unique solutions
STOC '98 Proceedings of the thirtieth 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
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Kolmogorov's Structure Functions with an Application to the Foundations of Model Selection
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
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
Distinguishing Complexity and Symmetry of Information
Distinguishing Complexity and Symmetry of Information
Compression of Samplable Sources
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Language Compression and Pseudorandom Generators
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On Pseudoentropy versus Compressibility
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On the optimal compression of sets in PSPACE
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Symmetry of information and nonuniform lower bounds
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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The information contained in a string x about a string y is the difference between the Kolmogorov complexity of y and the conditional Kolmogorov complexity of y given x, i.e., I(x : y)=C(y)-C(y|x). The Kolmogorov-Levin Theorem says that I(x : y) is symmetric up to a small additive term. We investigate if this property also holds for several versions of polynomial time-bounded Kolmogorov complexity.We study symmetry of information for some variants of distinguishing complexity CD where CD(x) is the length of a shortest program which accepts x and only x. We show relativized worlds where symmetry of information does not hold in a strong way for deterministic and nondeterministic polynomial time distinguishing complexities CDpoly and CNDpoly. On the other hand, for nondeterministic polynomial time distinguishing complexity with randomness, CAMDpoly, we show that symmetry of information holds for most pairs of strings in any set in NP. Our techniques extend work of Buhrman et al. (Language compression and pseudorandom generators, in: Proc. 19th IEEE Conf. on Computational Complexity, IEEE, New York, 2004, pp. 15-28) on language compression by AM algorithms, and have the following application to the compression of samplable sources, introduced in Trevisan et al. (Compression of sample sources, in: Proc. 19th IEEE Conf. on Computational Complexity, IEEE, New York, 2004, pp. 1-15): any element x in the support of a polynomial time samplable source X can be given a description of size - log Pr[X = x] + O(log3 n), from which x can be recovered by an AM algorithm.