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| Presentation | 2014-06-14 10:30 On Characterizations of Randomized Computation Using Plain Kolmogorov Complexity Shuichi Hirahara, Akitoshi Kawamura (Univ. of Tokyo)  COMP2014-12 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | 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, Kouck'y, 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 $PSPACE cap P/poly$. Next, we show that the class $DTTR_{C, alpha}$ obtained from $DTTR_C$ by imposing a restriction on the reduction lies between BPP and PSPACE. Finally, we show that the class $P/R_C^{=log}$ obtained by further restricting the reduction to ask queries of logarithmic length lies between BPP and $Sigma^P_2 cap P/poly$. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Kolmogorov complexity / Randomized computation / Truth-table reduction / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 114, no. 80, COMP2014-12, pp. 77-83, June 2014. | |
| Paper # | COMP2014-12 | |
| Date of Issue | 2014-06-06 (COMP) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | COMP2014-12 |
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| Conference Information | |
| Committee | COMP IPSJ-AL |
| Conference Date | 2014-06-13 - 2014-06-14 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Matsuyama, Ehime |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Paper Information | |
| Registration To | COMP |
| Conference Code | 2014-06-COMP-AL |
| Language | English (Japanese title is available) |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On Characterizations of Randomized Computation Using Plain Kolmogorov Complexity |
| Sub Title (in English) | |
| Keyword(1) | Kolmogorov complexity |
| Keyword(2) | Randomized computation |
| Keyword(3) | Truth-table reduction |
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| 1st Author's Name | Shuichi Hirahara |
| 1st Author's Affiliation | The University of Tokyo (Univ. of Tokyo) |
| 2nd Author's Name | Akitoshi Kawamura |
| 2nd Author's Affiliation | The University of Tokyo (Univ. of Tokyo) |
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| Speaker | Author-1 |
| Date Time | 2014-06-14 10:30:00 |
| Presentation Time | 25 minutes |
| Registration for | COMP |
| Paper # | COMP2014-12 |
| Volume (vol) | vol.114 |
| Number (no) | no.80 |
| Page | pp.77-83 |
| #Pages | 7 |
| Date of Issue | 2014-06-06 (COMP) |
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