Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 . >
['A. Chi-Chih Yao']
I am writing a research paper on a idea Algebraic decision trees and Euler characteristics
[{"from": "human", "value": "I am writing a research paper on a idea Algebraic decision trees and Euler characteristics"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 . >"}]