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Some lower and upper bounds for algebraic decision trees and the separation problem

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1 Author(s)
Vatan, F. ; Dept. of Math., Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA

The complexity of computing Boolean functions with algebraic decision trees over GF(2) and R is considered. Some lower and upper bounds for algebraic decision trees of various degrees are found. It is shown that over GF(2) decision trees of degree d are more powerful than trees of degree <d. For the case of decision trees over R, it is shown that decision trees of degree ⩾n/2-O(√n log O(1)n) are more powerful than trees of degree cn, with 0<c<1/2

Published in:

Structure in Complexity Theory Conference, 1992., Proceedings of the Seventh Annual

Date of Conference:

22-25 Jun 1992