Randomness, relativizations, and polynomial reducibilities
Proc. of the conference on Structure in complexity theory
Structural complexity 2
Polynomial-time reducibilities and “almost all” oracle sets
Theoretical Computer Science
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Computational depth and reducibility
Theoretical Computer Science
An observation on probability versus randomness with applications to complexity classes
Mathematical Systems Theory
The global power of additional queries to random oracles
Information and Computation
Selected papers of the eleventh symposium on Theoretical aspects of computer science
STACS '94 Selected papers of the eleventh symposium on Theoretical aspects of computer science
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
The quantitative structure of exponential time
Complexity theory retrospective II
Feasible reductions to Kolmogorov-Loveland stochastic sequences
Theoretical Computer Science
Separations by Random Oracles and "Almost" Classes for Generalized Reducibilities
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Resource-Bounded Balanced Genericity, Stochasticity and Weak Randomness
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Measure on small complexity classes, with applications for BPP
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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We consider separations of reducibilities by random sets. First, we show a result on polynomial-time bounded reducibilities which query their oracle non-adaptively: for every p-random set R, there is a set which is reducible to R with k+1 queries, but is not reducible to any other p-random set with at most k queries. This result solves an open problem stated in a recent survey paper by Lutz and Mayordomo [17]. Second, we show that the separation result above can be transferred from the setting of polynomial time bounds to a setting of rec-random sets and recursive reducibilities. This extends the main result of Book, Lutz, and Martin [8], who, by using different methods, showed a similar separation with respect to Martin-Löf-random sets. Moreover, in both settings we obtain similar separation results for truth-table versus bounded truthtable reducibility.