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Problems on the generation of finite models

  • Jian Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 814)

Abstract

Recently, the subject of model generation has received much attention. By model generation we mean the automated generation of finite models of a given set of logical formulas. In this note, we present some problems on the generation of finite models. The purpose is two-fold: (1) to offer some test problems for model generation programs; and (2) to show the potential applications of such programs. Some of the problems are easy, some are hard and even open. We also give a new result in combinatory logic, which says that the fragment {B, N 1 } does not possess the strong fixed point property.

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References

  1. [1]
    Burris, S., and Lee, S., “Tarski's high school identities,” The Amer. Math. Monthly 100 (1993) 231–236.Google Scholar
  2. [2]
    Fujita, M. et al, “Automatic generation of some results in finite algebra,” Proc. 13th IJCAI (1993) 52–57.Google Scholar
  3. [3]
    Hasegawa, R. et al, “'MGTP: A parallel theorem prover based on lazy model generation,” Proc. 11th CADE, LNAI 607 (1992) 776–780.Google Scholar
  4. [4]
    Kolesova, G. et al, “On the number of 8×8 Latin squares,” J. Combinatorial Theory A54 (1990) 143–148.Google Scholar
  5. [5]
    Manthey, R., and Bry, F.,“SATCHMO: A theorem prover implemented in Prolog,” Proc. 9th CADE, LNCS 310 (1988) 415–434.Google Scholar
  6. [6]
    McCune, W., “Single axioms for groups and Abelian groups with various operations,” J. Automated Reasoning 10 (1993) 1–13.Google Scholar
  7. [7]
    Peterson, J. G., “The possible shortest single axioms for EC-tautologies,” Report No. 105, Dept. of Mathematics, Univ. of Auckland (1977).Google Scholar
  8. [8]
    Slaney, J., “FINDER: Finite domain enumerator. Version 3.0 notes and guide,” Australian National University, (1993).Google Scholar
  9. [9]
    Winker, S., “Generation and verification of finite models and counterexamples using an automated theorem prover answering two open questions,” J. ACM 29 (1982) 273–284.Google Scholar
  10. [10]
    Winker, S., “Robbins algebra: Conditions that make a near-Boolean algebra Boolean,” J. Automated Reasoning 6 (1990) 465–489.Google Scholar
  11. [11]
    Wos, L. et al, “A new use of an automated reasoning assistant: Open questions in equivalential calculus and the study of infinite domains,” Artificial Intelligence 22 (1984) 303–356.Google Scholar
  12. [12]
    Wos, L. “Meeting the challenge of fifty years of logic,” J. Automated Reasoning 6 (1990) 213–232.Google Scholar
  13. [13]
    Wos, L., “The kernel strategy and its use for the study of combinatory logic,” J. Automated Reasoning 10 (1993) 287–343.Google Scholar
  14. [14]
    Zhang, H., and Stickel, M., “Implementing the Davis-Putnam method by tries,” submitted to AAAI-94.Google Scholar
  15. [15]
    Zhang, J., “Search for models of equational theories,” Proc. 3rd Int'l Conf. for Young Computer Scientists (ICYCS-93), Beijing (1993) 2.60–63.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jian Zhang
    • 1
  1. 1.Academia SinicaInstitute of SoftwareBeijingP.R.China

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