Abstract
For decision problems Π(B) defined over Boolean circuits using gates from a restricted set B only, we have Π(B)⩽mAC0Π(B′) for all finite sets B and B′ of gates such that all gates from B can be computed by circuits over gates from B′. In this note, we show that a weaker version of this statement holds for decision problems defined over Boolean formulae, namely that Π(B)⩽mNC2Π(B′∪{∧,∨}) and Π(B)⩽mNC2Π(B′∪{0,1}) for all finite sets B and B′ of Boolean functions such that all f∈B can be defined in B′.
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