Computer Search for Counterexamples to Wilkie’s Identity

  • Jian Zhang
Conference paper

DOI: 10.1007/11532231_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3632)
Cite this paper as:
Zhang J. (2005) Computer Search for Counterexamples to Wilkie’s Identity. In: Nieuwenhuis R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science, vol 3632. Springer, Berlin, Heidelberg

Abstract

Tarski raised the High School Problem, i.e., whether a set of 11 identities (denoted by HSI) serves as a basis for all the identities which hold for the natural numbers. It was answered by Wilkie in the negative, who gave an identity which holds for the natural numbers but cannot be derived from HSI. This paper describes some computer searching efforts which try to find a small model of HSI rejecting Wilkie’s identity. The experimental results show that such a model has at least 11 elements. Some experiences are reported, and some issues are discussed.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jian Zhang
    • 1
  1. 1.Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesP.R.China

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