Every sequence is reducible to a random one
Information and Control
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
A pseudorandom oracle characterization of BPP
SIAM Journal on Computing
An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
On Languages Reducible to Algorithmically RandomLanguages
SIAM Journal on Computing
An observation on probability versus randomness with applications to complexity classes
Mathematical Systems Theory
The quantitative structure of exponential time
Complexity theory retrospective II
A Generalization of Resource-Bounded Measure, With an Application (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Applications of recursive operators to randomness and complexity
Applications of recursive operators to randomness and complexity
On the Construction of Effective Random Sets
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Autoreducibility of Random Sets: A Sharp Bound on the Density of Guessed Bits
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
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A language A ⊆ {0,1}* is called i.o. autoreducible if A is Turing-reducible to itself via a machine M such that, for infinitely many input words w, M does not query its oracle A about w. We examine the question if algorithmically random languages in the sense of Martin-Löf are i.o. autoreducible. We obtain the somewhat counterintuitive result that every algorithmically random language is polynomial-time i.o. autoreducible where the autoreducing machine poses its queries in a "quasi-nonadaptive" way; however, if in the above definition the "infinitely many" is replaced by "almost all," then every algorithmically random language is not autoreducible in this stronger sense. Further results obtained give upper and lower bounds on the number of queries of the autoreducing machine M and the number of inputs w for which M does not query the oracle about w.