Majority gates vs. general weighted threshold gates
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A single threshold gate with weights cannot in general be replaced by a polynomial fan-in unweighted threshold gate of parity gates.
On the other hand it can be replaced by a depth 2 unweighted threshold circuit of polynomial size. An extension of this construction is used to prove that whatever can be computed by a depthd polynomial size threshold circuit with weights can be computed by a depthd+1 polynomial size unweighted threshold circuit, whered is an arbitrary fixed integer.
A polynomial fan-in threshold gate (with weights) of parity gates cannot in general be replaced by a depth 2 unweighted threshold circuit of polynomial size.
Key wordscircuit complexity majority circuits threshold circuits lower bounds
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