@article{Fleischer1999DecisionTO,
title={Decision Trees: Old and New Results},
author={Rudolf Fleischer},
journal={Inf. Comput.},
year={1999},
volume={152},
pages={44-61}
}

Abstract In this paper, we prove two general lower bounds for algebraic decision trees which test membership in a set S ⊆ R n which is defined by linear inequalities. Let rank( S ) be the maximal dimension of a linear sub- space contained in the closure of S (in Euclidean topology). First we show that any decision tree for S which uses products of linear functions (we call such functions mlf- functions ) must have depth at least n −rank( S ). This solves an open question raised by A. C. Yao and… CONTINUE READING