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Some results on decision trees with relations to computational trees

  • Jerzy W. Jaromczyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 208)

Abstract

In this paper we have shown some results for decision trees with tests from the essentially wider class of functions than the polynomials of bounded degree.

We introduced the notion of functions r-distant to Rd[x] and have shown how starting from decision trees we can derive lower bounds in the model of computation trees. This relation suggests an uniform approach to lower bound proving in decision and computational tree models.

Keywords

Decision Tree Lower Bound Auxiliary Variable Computation Tree Membership Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Ben-Or,M., Lower bounds for algebraic computation trees, Proc. of the 15-th STOC, Boston, 1983, 80–86.Google Scholar
  2. [2]
    Jaromczyk,J.W.,Lower bounds for polygon simplicity testing and other problems, Lecture Notes in Computer Science v.176, 1984Google Scholar
  3. [3]
    Jaromczyk,J.W., Computational complexity in the model of decision trees, Warsaw, April 1984 (in polish).Google Scholar
  4. [4]
    Milnor, J., On the Betti numbers of real algebraic varieties, Proc. AMS 15, 1964, 275–280.Google Scholar
  5. [5]
    Steele, J.M., Yao, A.C., Lower bounds for algebraic decision trees, J.Algorithms 3, 1982, 1–8.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Jerzy W. Jaromczyk
    • 1
  1. 1.Institute of InformaticsWarsaw University, PKiN VIII p.WarsawPoland

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