Volume 2014

A composition theorem for decision tree complexity

Ashley Montanaro
Department of Computer Science
University of Bristol
Bristol, UK
ashley AT cs DOT bris DOT ac DOT uk

July 17, 2014

Abstract

We completely characterise the complexity in the decision tree model of computing composite relations of the form $h = g \circ (f^1,\dots,f^n)$, where each relation $f^i$ is boolean-valued. Immediate corollaries include a direct sum theorem for decision tree complexity and a tight characterisation of the decision tree complexity of iterated boolean functions.

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