Graphs and Circuits: Some Further Remarks

We consider the power of single level circuits in the context of graph complexity. We first prove that the single level conjecture fails for fanin-2 circuits over the basis { ,^,1}. This shows that the (surpisingly tight) phenomenon, established by Mirwald and Schnorr (1992) for quadratic functions, has no analogon for graphs. We then show that the single level conjecture fails for unbounded fanin circuits over {_,^,1}. This partially

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