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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 (Unpublished)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:
DateEvent
January 1991Completion
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Status: Not Peer Reviewed
Publication Status: Unpublished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.&nbsp;Paterson and U.&nbsp;Zwick, &ldquo;Shrinkage of de Morgan Formulae under Restriction&rdquo;, <i>Random Structures and Algorithms</i> <b>4</b>, pp.&nbsp;135-150 (1993)
Funder: European Strategic Programme of Research and Development in Information Technology (ESPRIT)
Grant number: 3075 (ESPRIT)
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