TY - GEN

T1 - Reductions to the set of random strings

T2 - 37th International Symposium on Mathematical Foundations of Computer Science 2012, MFCS 2012

AU - Allender, Eric

AU - Buhrman, Harry

AU - Friedman, Luke

AU - Loff, Bruno

PY - 2012

Y1 - 2012

N2 - This paper is motivated by a conjecture [1,5] that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [5] to settle this conjecture cannot succeed without significant alteration, but that it does bear fruit if we consider time-bounded Kolmogorov complexity instead. We show that if a set A is reducible in polynomial time to the set of time-t-bounded Kolmogorov-random 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.

AB - This paper is motivated by a conjecture [1,5] that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out in [5] to settle this conjecture cannot succeed without significant alteration, but that it does bear fruit if we consider time-bounded Kolmogorov complexity instead. We show that if a set A is reducible in polynomial time to the set of time-t-bounded Kolmogorov-random 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.

UR - http://www.scopus.com/inward/record.url?scp=84865013329&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-32589-2_11

DO - 10.1007/978-3-642-32589-2_11

M3 - Conference contribution

AN - SCOPUS:84865013329

SN - 9783642325885

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 88

EP - 99

BT - Mathematical Foundations of Computer Science 2012 - 37th International Symposium, MFCS 2012, Proceedings

Y2 - 27 August 2012 through 31 August 2012

ER -