A Comparison of the Computational Power of Sigmoid and Boolean Threshold Circuits
نویسندگان
چکیده
We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with linear threshold gates). On the other hand it turns out that, for any constant depth d, polynomial size sigmoid threshold circuits with polynomially bounded weights compute exactly the same boolean functions as the corresponding circuits with linear threshold gates. ∗Partially supported by NSF-CCR-8805978 and AFOSR-87-0400 †Partially supported by Siemens Corporate Research and AFOSR-88-0235 and AFOSR-91-0343
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On the Computational Power of Sigmoid versus Boolean Threshold Circuits
We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with boolean threshold gates). On the other hand it turns out that, for any constant depth d , polynomial size sigmoid...
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