Published by the Department of Computer Science, The University of Chicago.
A composition theorem for decision tree complexity
Department of Computer Science
University of Bristol
ashley AT cs DOT bris DOT ac DOT uk
July 17, 2014
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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Submitted March 1st 2013, revised June 25, 2013 and in final form July 15, 2014, published July 17, 2014.