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Shrinkage of de Morgan formulae under restriction
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Paterson, Michael S. and Zwick, Uri (1991) Shrinkage of de Morgan formulae under restriction. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)
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Abstract
It is shown that a random restriction leaving only a fraction epsilon of the input variables unassigned reduces the expected de Morgan formula size of the induced function by at least a factor of epsilon((5-sqrt(3))/2) ~= epsilon 1.63. (A de Morgan formula is a formula over the basis {/\, \/, ~}.) This improves a long-standing result of epsilon 1.5 by Subbotovskaya and a recent improvement to epsilon((21-sqrt(73))/8) ~= epsilon 1.55 by Nisan and Impagliazzo. The new exponent yields an increased lower bound of omega(n((7-sqrt(3))/2-O(1)) for the de Morgan formula size of a function defined by Andreev. This is the largest lower bound known for a function in NP.
| Item Type: | Report | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Proposition (Logic) | ||||
| Series Name: | Department of Computer Science research report | ||||
| Publisher: | University of Warwick. Department of Computer Science | ||||
| Official Date: | January 1991 | ||||
| Dates: |
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| Number: | Number 171 | ||||
| Number of Pages: | 9 | ||||
| DOI: | CS-RR-171 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Reuse Statement (publisher, data, author rights): | M.S. Paterson and U. Zwick, “Shrinkage of de Morgan Formulae under Restriction”, <i>Random Structures and Algorithms</i> <b>4</b>, pp. 135-150 (1993) | ||||
| Funder: | European Strategic Programme of Research and Development in Information Technology (ESPRIT) | ||||
| Grant number: | 3075 (ESPRIT) | ||||
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