TY - JOUR
T1 - On characterizations of randomized computation using plain Kolmogorov complexity
AU - Hirahara, Shuichi
AU - Kawamura, Akitoshi
N1 - Publisher Copyright:
© 2018 - IOS Press and the authors. All rights reserved.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018
Y1 - 2018
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 BPP, a lower bound 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 DTTRC,α obtained from DTTRC by imposing a super-constant minimum query length restriction on the reduction lies between BPP and PSPACE. Finally, we show that the class P/RCt =log obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and ∑2 p ∩ 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 BPP, a lower bound 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 DTTRC,α obtained from DTTRC by imposing a super-constant minimum query length restriction on the reduction lies between BPP and PSPACE. Finally, we show that the class P/RCt =log obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and ∑2 p ∩ P/poly.
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U2 - 10.3233/COM-170075
DO - 10.3233/COM-170075
M3 - Article
AN - SCOPUS:85050924980
VL - 4
SP - 45
EP - 56
JO - Bladder Cancer
JF - Bladder Cancer
SN - 2352-3727
IS - 1
ER -