The Pattern Basis Approach to Circuit Complexity

Bruce K. Smith

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arXiv · 1606.05331

The Pattern Basis Approach to Circuit Complexity

Bruce K. Smith

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Abstract

We describe and motivate a proposed new approach to lowerbounding the circuit complexity of boolean functions, based on a new formalization of "patterns" as elements of a special basis of the vector space of all truth table properties. We prove that a "pattern basis" with certain properties would lead to a useful complexity formula of a specific form, and speculate on how to find such a basis. This formula might take as long to compute on arbitrary functions as a brute-force search among circuits, thus addressing the natural proofs barrier, but has a form amenable to proving lower bounds for well-understood explicit functions.

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Bruce K. Smith. 2016-06-16. The Pattern Basis Approach to Circuit Complexity. https://arxiv.org/abs/1606.05331

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