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Pseudorandom numbers and their Application to Stochastic Numerical Analysis

Research Project

Project/Area Number 10640117
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOkayama 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)
Keywordspseudorandom 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.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report

Research Products

(31 results)

All Other

All Publications (31 results)

  • [Publications] Takashima, K.: "Hybrid bseudcrandom number generation"Monte Carlo Methods and Applications. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashima, K.: "Random walk tests and Feedback Polynomials of mseguences"Proceedings of Fifth International Confereuce on Pattern recognition and Information. 1. 267-271 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashima, K.: "Random walk tests of pseudorandom number generation by cellular auto mata"Proceedings of the 3-rd St. Petersburg Workshop on slmulation. 302-305 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 高嶋 恵三: "擬似乱数とrandom walk検定"計算機統計学. 11. 35-44 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Takashima, K.: "Random walk tests and pseudorandom number generation"Proceedings of International Conterence of Mathematical Analysis and Appications. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Munemasa, A.: "Orthogonal arrays, pri*sitive trinomials, and shift-register sequences"Finite Fields and Their Applications. 4. 252-260 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 掘田 良之: "岩波書店"環と体1. 193 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 掘田 良之: "岩波書店"環と体2. 168 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Takashima: "Pseudorandom numbers and random walk tests"Computer Statistics. 11(in Jaoanese). 35-44 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Takashima: "Random walk tests of pseudorandom number generation by cellular automata"Proceedings of 3-rd St. Peterbug Workshop on Simulation. 302-305 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Takashima: "Random walk tests and Feedback Polynomials of m-sequences"Proceedings of Fifth International Conference on Pattren Recognition and Information Processing. 1. 267-271 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. Sugimura and K. Takashima: "On a Fractal Approarch to Actual to Actual Plant Images"Proceedings of Fifth International Conference on Pattern Recognition and Information Processing. 2. 134-138 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Takashima: "Hybrid pseudorandom number generation"Monte Carlo Methods and Applications. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] K. Takashima: "Random walk tests and pseudorandom number generation"Preceedings of International Conference of Mathematical Analysis and Applications. (to Appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Munemasa: "Orthogonal arrays, primitive trinomails, and shift-register sequences"Finite Fields and Their Applications. 4. 252-260 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 高嶋恵三: "擬似乱数とrandom walk検定"計算機統計学. 11. 35-44 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Keizo Takashima: "Random walk test and Feedback Polynomials of m-sequences"Proceeding of Fifth International Conference in Pattern Recognition. 1. 267-271 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.sugimura,,K.Takeshima: "On a Fractal Approach to Actural Plant Images"Proceeding of Fifth International Conference in Pattern Recognition and Information Proceeding. 2. 134-138 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Munemasa: "Flag-transitive 2-designs arising from line-spreals"Geometriae Dedicata. 77. 209-213 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Munemasa,S.T.Daugherty,et al: "Type IV Self-Ducel Codes over Rings"IEEE Trans.Inform,Theory. 45. 2345-2360 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Munemasa,M.kitazume: "New 5-designs with automorphism group PSL(2,23)"J.Combinatorial Designs. 7. 147-155 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 掘田良之: "岩波書店"環と体1. 193 (1997)

    • Related Report
      1999 Annual Research Report
  • [Publications] 掘田良之: "岩波書店"環と体2. 168 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] Takashima,K.: "Random walk tests of pseudorandom number generations by cellular automata" Proceedings of the 3-rd St.Peterburg Workshop on Simulation. 302-305 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Takashima,K.: "Random walk tests and Pseudorandom number generators" Proceedings of International Conference of Mathematical Analysis and Applications. (掲載予定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 高嶋恵三: "擬似乱数とrandom walk検定" 計算機統計学. 掲載予定 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 高嶋恵三: "Cellular Automaton擬似乱数に対するRandom Walk検定" 数理解析研究所講究録. 1032. 148-151 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Munemasa,A.: "Orthogonal arrays,primitive trinomials,and shift-register sequences" Finite Fields and Their Applications. 4. 252-260 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Munemasa,A.: "Duality maps of finite abelian groups and their applications to spin models" J.Algebraic Combinatorics. 18. 223-233 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 堀田 良之: "環と体 2(体論)" 岩波書店, (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 堀田良之: "簡約群の表現論" 日本評論社, (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-03-31   Modified: 2016-04-21  

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