Optimal direct sum results for deterministic and randomized decision tree complexity

Authors:
Rahul Jain;Hartmut Klauck;Miklos Santha
Affiliations:
Centre for Quantum Technologies and Department of Computer Science, National University of Singapore, Singapore;Centre for Quantum Technologies (NUS) and School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore;CNRS, LRI, Université Paris-Sud, Orsay, France and Centre for Quantum Technologies, National University of Singapore, Singapore
Venue:
Information Processing Letters
Year:
2010

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Abstract

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.