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I’m recently active in stack exchange. (http://cstheory.stackexchange.com/) I’ve decided to refine the paper according to the discussions there. The definition of sparsity will be more generalized.

The sticky post on the top collects all the related links. Especially, the google docs include extra explanations.

I’ll keep updating them on weekly basis.

I also gathered my old Hamming distance papers in the sticky post. Their motivation was actually this research: Let’s say a node in a Boolean circuit is an AND gate a=a_{1} ∧ a_{2 }. An l-clique c is *generated at* a if the edges of c implies a. Inductively we have two sets of l-cliques generated at a_{1} and a_{2 }. It takes a theory to figure out which cliques are generated at a. I first thought minimum Hamming distance could tell something important about it. It was short for the clique complexity. I moved to the l-extension after doing hard research.

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