Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Structural complexity 2
Almost everywhere high nonuniform complexity
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.)
The quantitative structure of exponential time
Complexity theory retrospective II
Separating Complexity Classes Using Autoreducibility
SIAM Journal on Computing
Introduction to Coding Theory
A Generalization of Resource-Bounded Measure, with Application to the BPP vs. EXP Problem
SIAM Journal on Computing
On the Autoreducibility of Random Sequences
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
On the Construction of Effective Random Sets
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations 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
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A set A 驴 {0, 1}* is called i.o. Turing-autoreducible if A is reducible to itself via an oracle Turing machine that never queries its oracle at the current input, outputs either A(x) or a don't-know symbol on any given input x, and outputs A(x) for infinitely many x. If in addition the oracle Turing machine terminates on all inputs and oracles, A is called i.o. truth-table autoreducible. Ebert and Vollmer obtained the somewhat counterintuitive result that every Martin-L枚f random set is i.o. truth-table-autoreducible and investigated the question of how dense the set of guessed bits can be when i.o. autoreducing a random set.We show that rec-random sets are never i.o. truth-table-autoreducible such that the set of guessed bits has strictly positive constant density in the limit, and that a similar assertion holds for Martin-L枚f random sets and i.o. Turing-autoreducibility. On the other hand, our main result asserts that for any computable function r that goes non-ascendingly to zero, any rec-random set is i.o. truth-table-autoreducible such that the set of guessed bits has density bounded from below by r(m).