Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

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On a hierarchy of Boolean functions hard to compute in constant depth

Anna Bernasconi


Any attempt to find connections between mathematical properties and complexity has a strong relevance to the field of Complexity Theory. This is due to the lack of mathematical techniques to prove lower bounds for general models of computation.
This work represents a step in this direction: we define a combinatorial property that makes Boolean functions ``hard'' to compute in constant depth and show how the harmonic analysis on the hypercube can be applied to derive new lower bounds on the size complexity of previously unclassified Boolean functions.

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