The gap between monotone and non-monotone circuit complexity is exponential (Q1813126)
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scientific article; zbMATH DE number 2501
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The gap between monotone and non-monotone circuit complexity is exponential |
scientific article; zbMATH DE number 2501 |
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The gap between monotone and non-monotone circuit complexity is exponential (English)
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25 June 1992
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A. A. Razborov has shown that there exists a polynomial time computable monotone Boolean function whose monotone circuit complexity is at least \(n^{c\log n}\). We observe that this lower bound can be improved to \(\exp(cn^{1/6-o(1)})\). The proof is immediate by combining the Alon- Boppana version of another argument of Razborov with results of Grötschel-Lovász-Schrijver on the Lovász-capacity \(\delta\) of a graph.
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