Optimal Direct Sum Results for Deterministic and Randomized Decision Tree Complexity

A Direct Sum Theorem holds in a model of computation, when for every problem solving some k input instances together is k times as expensive as solving one. We show that Direct Sum Theorems hold in the models of deterministic and randomized decision trees for all relations. We also note that a near optimal Direct Sum Theorem holds for quantum decision trees for boolean functions.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Rahul Jain, Hartmut Klauck, Miklos Santha
• Keywords: CORR 2010, Direct Sum Theorem, Education, Input Instances, Optimal Direct Sum