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Polynomial Hierarchy, Betti Numbers, and

✍ Scribed by Saugata Basu; Thierry Zell


Publisher
Springer-Verlag
Year
2010
Tongue
English
Weight
648 KB
Volume
10
Category
Article
ISSN
1615-3375

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We show that any algebraic computation tree or any fixed-degree algebraic tree for solving the membership question of a compact set S R n must have height greater than 0(log(; i (S)))&cn for each i, where ; i (S) is the ith Betti number. This generalizes a well-known result by Ben-Or who proved this