期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：1995
卷号：1995
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We extend the lower bounds on the depth of algebraic decision trees
to the case of {\em randomized} algebraic decision trees (with
two-sided error) for languages being finite unions of hyperplanes
and the intersections of halfspaces, solving a long standing open
problem. As an application, among other things, we derive, for the
first time, an (n2) {\em randomized} lower bound for the
{\em Knapsack Problem} which was previously only known for
deterministic algebraic decision trees. It is worth noting that for
the languages being finite unions of hyperplanes our proof method
yields also a new elementary technique for deterministic algebraic
decision trees without making use of Milnor's bound on Betti number
of algebraic varieties.
