Abstract
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.
| Original language | English |
|---|---|
| Title of host publication | Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings |
| Publisher | Springer Verlag |
| Pages | 348-359 |
| Number of pages | 12 |
| Edition | PART 2 |
| ISBN (Print) | 9783662444641 |
| DOIs | |
| Publication status | Published - Jan 1 2014 |
| Event | 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 - Budapest, Hungary Duration: Aug 25 2014 → Aug 29 2014 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Number | PART 2 |
| Volume | 8635 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014 |
|---|---|
| Country | Hungary |
| City | Budapest |
| Period | 8/25/14 → 8/29/14 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
On characterizations of randomized computation using plain Kolmogorov complexity. / Hirahara, Shuichi; Kawamura, Akitoshi.
Mathematical Foundations of Computer Science 2014 - 39th International Symposium, MFCS 2014, Proceedings. PART 2. ed. Springer Verlag, 2014. p. 348-359 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8635 LNCS, No. PART 2).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - On characterizations of randomized computation using plain Kolmogorov complexity
AU - Hirahara, Shuichi
AU - Kawamura, Akitoshi
PY - 2014/1/1
Y1 - 2014/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84906264560&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84906264560&partnerID=8YFLogxK
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
ER -