Abstract
For any set S contained in R/sup n/, let chi (S) denote its Euler characteristic. The author shows that any algebraic computation tree or fixed-degree algebraic decision tree must have height Omega (log mod chi (S) mod )for deciding the membership question of a compact semi-algebraic set S. This extends a result by A. Bjorner, L. Lovasz and A. Yao where it was shown that any linear decision tree for deciding the membership question of a closed polyhedron S must have height greater than or equal to log/sub 3/ mod chi (S) mod .< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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