Journal of Applied and Industrial Mathematics

, Volume 11, Issue 1, pp 130–144 | Cite as

On teaching sets for 2-threshold functions of two variables

  • E. M. Zamaraeva


We consider k-threshold functions of n variables, i.e. the functions representable as the conjunction of k threshold functions. For n = 2, k = 2, we give upper bounds for the cardinality of the minimal teaching set depending on the various properties of the function.


machine learning threshold function teaching dimension teaching set 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Yu. Zolotykh and V. N. Shevchenko, “Estimating the Complexity of Deciphering a Threshold Function in a k-Valued Logic,” Zh. Vychisl. Mat. Mat. Fiz. 39 (2), 346–352 (1999) [Comput. Math. Math. Phys. 39 (2), 328–334 (1999)].MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. N. Shevchenko and N. Yu. Zolotykh, “On the Complexity of Deciphering the Threshold Functions of k-Valued Logic,” Dokl. Akad. Nauk 362 (5), 606–608 (1998) [Dokl. Math. 58 (2), 268–270 (1998)].MathSciNetzbMATHGoogle Scholar
  3. 3.
    M. A. Alekseyev, M. G. Basova, and N. Yu. Zolotykh, “On the Minimal Teaching Sets of Two-Dimensional Threshold Functions,” SIAMJ. DiscreteMath. 29 (1), 157–165 (2015).MathSciNetzbMATHGoogle Scholar
  4. 4.
    M. Anthony, G. Brightwell, and J. Shawe-Taylor, “On Specifying Boolean Functions by Labelled Examples,” Discrete Appl. Math. 61 (1), 1–25 (1995).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    W. J. Bultman and W. Maass, “Fast Identification of Geometric Objects with Membership Queries,” Inform. Comput. 118 (1), 48–64 (1995).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    A. Yu. Chirkov and N. Yu. Zolotykh, “On the Number of Irreducible Points in Polyhedra,” Graphs Combin. 32 (5), 1789–1803 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    V. N. Shevchenko and N. Yu. Zolotykh, “Lower Bounds for the Complexity of Learning Half-Spaces with Membership Queries,” in Algorithmic Learning Theory (Proceedings of 9th International Conference, Otzenhausen, Germany, October 8–10, 1998) (Springer, Berlin, 1998), pp. 61–71.CrossRefGoogle Scholar
  8. 8.
    J. Trainin, “An Elementary Proof of Pick’s Theorem,” Math. Gaz. 91 (522), 536–540 (2007).CrossRefGoogle Scholar
  9. 9.
    E. Zamaraeva, “On Teaching Sets of k-Threshold Functions,” Inform. and Comput. 251, 301–313 (2016).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Lobachevsky Nizhny Novgorod State UniversityNizhny NovgorodRussia

Personalised recommendations