TY - GEN

T1 - On characterizations of randomized computation using plain Kolmogorov complexity

AU - Hirahara, Shuichi

AU - Kawamura, Akitoshi

PY - 2014

Y1 - 2014

N2 - Allender, Friedman, and Gasarch recently proved an upper bound of pspace for the class DTTR K of decidable languages that are polynomial-time truth-table reducible to the set of prefix-free Kolmogorov-random strings regardless of the universal machine used in the definition of Kolmogorov complexity. It is conjectured that DTTR K in fact lies closer to its lower bound BPP established earlier by Buhrman, Fortnow, Koucký, and Loff. It is also conjectured that we have similar bounds for the analogous class DTTR C defined by plain Kolmogorov randomness. In this paper, we provide further evidence for these conjectures. First, we show that the time-bounded analogue of DTTR C sits between BPP and pspace ∩ P/poly. Next, we show that the class DTTR C, α obtained from DTTR C by imposing a restriction on the reduction lies between BPP and pspace. Finally, we show that the class P/R obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and P/poly.

AB - Allender, Friedman, and Gasarch recently proved an upper bound of pspace for the class DTTR K of decidable languages that are polynomial-time truth-table reducible to the set of prefix-free Kolmogorov-random strings regardless of the universal machine used in the definition of Kolmogorov complexity. It is conjectured that DTTR K in fact lies closer to its lower bound BPP established earlier by Buhrman, Fortnow, Koucký, and Loff. It is also conjectured that we have similar bounds for the analogous class DTTR C defined by plain Kolmogorov randomness. In this paper, we provide further evidence for these conjectures. First, we show that the time-bounded analogue of DTTR C sits between BPP and pspace ∩ P/poly. Next, we show that the class DTTR C, α obtained from DTTR C by imposing a restriction on the reduction lies between BPP and pspace. Finally, we show that the class P/R obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and P/poly.

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U2 - 10.1007/978-3-662-44465-8_30

DO - 10.1007/978-3-662-44465-8_30

M3 - Conference contribution

AN - SCOPUS:84906264560

SN - 9783662444641

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

SP - 348

EP - 359

BT - Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings

PB - Springer Verlag

T2 - 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014

Y2 - 24 August 2014 through 28 August 2014

ER -