Decision Trees: Old and New Results

  title={Decision Trees: Old and New Results},
  author={Rudolf Fleischer},
  journal={Inf. Comput.},
  • Rudolf Fleischer
  • Published 1999
  • Computer Science, Mathematics
  • Inf. Comput.
  • 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
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