Abstract
Andrew Yao proved some lower bounds for algebraic computation trees with integer inputs. In his key result he proved bounds on the number of components of the leaf space of a homogeneous decision tree derived from a computation tree. In this paper we present a shorter and more conceptual proof. We introduce the concept of aregulated tree as a generalization of a regular tree which has the advantage of allowing the same lower bounds on the non-linear portion of the complexity. The proof is an application of a result of Ben-Or.
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Hirsch, M.D. Lower bounds for the non-linear complexity of algebraic computation trees with integer inputs. Comput Complexity 1, 257–268 (1991). https://doi.org/10.1007/BF01200063
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DOI: https://doi.org/10.1007/BF01200063