| Project/Area Number |
10640117
|
|---|
| 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 | Okayama University of Science |
|---|
Principal Investigator |
TAKASHIMA Keizo Faculty of Science, Okayama University of Science, 理学部, 教授 (00137184)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OGAWA Shigeyoshi Faculty of Technology, Kanazawa University, 工学部, 教授 (80101137)
HOTTA Ryoushi Faculty of Science, Okayama University of Science, 理学部, 教授 (70028190)
TAKENAKA Shigeo Faculty of Science, Okayama University of Science, 理学部, 教授 (80022680)
MUNEMASA Akihoro Graduate School of Mathematics, Kyushu University, 大学院・数理学研究科, 助教授 (50219862)
HIKIDA Masato Faculty of Science, Okayama University of Science, 理学部, 助教授 (10098593)
兵頭 義史 岡山理科大学, 理学部, 助教授 (90189811)
|
|---|
| Project Period (FY) |
1998 – 1999
|
| Project Status |
Completed (Fiscal Year 1999)
|
| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
|
|---|
| Keywords | pseudorandom numbers / stochastic numerical analysis / random walk / finite algebra / statistical tests |
|---|
| Research Abstract |
We introduce statistical tests for pseudorandom number generations, which are based on functionals of sample paths of 1-dimensional random walks. Using these methods, we test statistically the following pseudorandom number generators : m-sequences, additive number generators, and cellular automata generators. The results of random walk tests detect statistical biases of these generators. Moreover, from the results, we can find some conjectures, for example,
● the multiples of a trinomial f over GF(2) are only those having the form such as square of f and so on, while the degrees of multiles are not so large. This conjecture has been proved by Munemasa, in case that the degree of multiples are less than or equal to the twice of the degree of f.
● A primitive polynomial over GF(2) and its reciprocal polynomial must have different algebraic properties. This conjecture is assured by the results of maximum tests, and sojourn time tests.
|
