2000 Fiscal Year Final Research Report Summary
Computability and polynomial time computability
| Project/Area Number |
11640112
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
MATSUBARA Yo Nagoya univ., school of info. & sci., ass.prof., 情報文化学部, 助教授 (30242788)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OZAWA Masanao Nagoya univ., school of info. & sci., ass.prof., 情報文化学部, 教授 (40126313)
YOSHINOBU Yasuo Nagoya univ., grad.school of human info., ass., 大学院・人間情報学研究科, 助手 (90281063)
TSUKIJI Tatsuie Nagoya univ., school of info. & sci., ass.prof., 情報文化学部, 助手 (70291961)
SATO Junya Nagoya univ., grad.school of human info., ass.prof., 人間情報学研究科, 助教授 (20235352)
IHARA Shunsuke Nagoya univ., school of info. & sci., ass.prof., 情報文化学部, 教授 (00023200)
|
|---|
| Project Period (FY) |
1999 – 2000
|
| Keywords | computational complexty / recursive functions / learning / set theory |
|---|
| Research Abstract |
The field of recursion and polynomial-time computational complexity theories are closely related to a wide range of topics including set theory, complexity theory, learning theory, and probability methods for algorithms and quantum computing theory. Here we report our work ranging over these topics.
The Computational complexity of Generalized Tsume-Shogi : The Generalized Tsume-Shogi problem uses the extended board of size n×n for a natural number n, rather than the usual 8×8 size. We show that solving GTS is EXPTIME-complete. As a corollary, Generalized Shogi is also proved to be EXPTIME-complete.
Probability methods for algorithms : The number of outputs of randomly generated circuits of size n is shown to obey a normal distribution of mean n/3 and variance √<3n/45>.
Learning 1 : We consider the problem of learning a consistent hypothesis of monotone Boolean conjunction of length O (logn), given negative examples of length n. This problem is shown to be computationally equivalent to the satisfiability problem of AND-OR-AND Boolean circuits having O ((logn)^2) inputs with respect to log-space many-one reducibility. Learning 2 : Applying the inclusion-exclusion principle, we show that the class of poly n-size DNF formula can be learnable within time 2^<0(√<n>)>. Moreover, this learning time is shown to be almost the best possible in the agnostic learning model.
Learning 3 : Learning general Boolean functions depending on O(logn) variables is discussed. Three fast algorithms finding O(logn) relevant variables are presented.
Y.Matsubara and S.Shelah proved that if λ is a strong limit singular cardinal then the non-stationary ideal over P_κλ is nowhere precipitous. They also proved that Means' Conjecture holds under the same hypothesis. T.〜Ishiu and Yoshinobu showed that for any infinite cardinal κ, every κ^+-strategically closed poset is κ^+-strategically closed if and only if square-κholds.
|
