An Automated Deduction and Its Implementation for Solving Problem of Sequence at University Entrance Examination

  • Yumi Wada
  • Takuya Matsuzaki
  • Akira Terui
  • Noriko H. Arai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)


“Todai Robot Project” is a project of artificial intelligence launched by National Institute of Informatics for re-unifying the artificial intelligence field subdivided in 1980s and afterwards. We focus towards attaining a high score in National Center Test for University Admissions, and use Quantifier Elimination (QE) over the real closed fields as a main tool for solving problems in mathematics. However, it is not applicable for several kinds of problems such as one with sequence. In this article, we propose an algorithm for solving problems of sequence at the National Center Test for University Admissions.


Automated deduction Recurrence relations Sequences 


  1. 1.
    Agarwal, R.P.: Difference Equations and Inequalities: Theory, Methods, and Applications, 2nd edn. Marcel Dekker, New York (2000)zbMATHGoogle Scholar
  2. 2.
    Arai, N.H.: The impact of AI: can a robot get into the University of Tokyo? Natl. Sci. Rev. 2(2), 135–136 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Arai, N.H., Matsuzaki, T., Iwane, H., Anai, H.: Mathematics by machine. In: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation – ISSAC 2014, pp. 1–8. ACM, New York (2014)Google Scholar
  4. 4.
    Bundy, A.: The automation of proof by mathematical induction. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, 2nd edn, pp. 845–911. North-Holland, Amsterdam (2001)CrossRefGoogle Scholar
  5. 5.
    Matsuzaki, T., Iwane, H., Anai, H., Arai, N.H.: The most uncreative examinee: a first step toward wide coverage natural language math problem solving. In: Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence, pp. 1098–1104 (2014)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yumi Wada
    • 1
  • Takuya Matsuzaki
    • 2
  • Akira Terui
    • 1
  • Noriko H. Arai
    • 3
  1. 1.University of TsukubaTsukubaJapan
  2. 2.Nagoya UniversityNagoyaJapan
  3. 3.National Institute of InformaticsTokyoJapan

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