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Reductions to the set of random strings: The resourcebounded case
 in Proc. 37th International Symposium on Mathematical Foundations of Computer Science (MFCS ’12), 2012, Lecture Notes in Computer Science
"... ABSTRACT. This paper is motivated by a conjecture [All12, ADF+13] that BPP can be characterized in terms of polynomialtime nonadaptive reductions to the set of Kolmogorovrandom strings. In this paper we show that an approach laid out in [ADF+13] to settle this conjecture cannot succeed without sig ..."
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ABSTRACT. This paper is motivated by a conjecture [All12, ADF+13] that BPP can be characterized in terms of polynomialtime nonadaptive reductions to the set of Kolmogorovrandom strings. In this paper we show that an approach laid out in [ADF+13] to settle this conjecture cannot succeed without significant alteration, but that it does bear fruit if we consider timebounded Kolmogorov complexity instead. We show that if a setA is reducible in polynomial time to the set of timetbounded Kolmogorovrandom strings (for all large enough time bounds t), then A is in P/poly, and that if in addition such a reduction exists for any universal Turing machine one uses in the definition of Kolmogorov complexity, then A is in PSPACE. 1.
MINIMAL PAIRS IN THE C.E. TRUTHTABLE DEGREES.
"... Strong reducibilities such as the mreducibility have been around implicitly, if not explicitly, since the dawn of computability theory. The explicit recognition of the existence of differing kinds of oracle access mechanisms began with the seminal work of Post [12]. Of interest to us from Post’s pa ..."
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Strong reducibilities such as the mreducibility have been around implicitly, if not explicitly, since the dawn of computability theory. The explicit recognition of the existence of differing kinds of oracle access mechanisms began with the seminal work of Post [12]. Of interest to us from Post’s paper are the socalled tabular reducibilities ≤tt, truth table reducibility, and
REDUCTIONS TO THE SET OF RANDOM STRINGS:
, 2012
"... Vol. 10(3:5)2014, pp. 1–18 www.lmcsonline.org ..."