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On the frequency of the most frequently occurring variable in dual monotone DNFs

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Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = RULIB-FS)
Other
Genre (authority = marcgt)
technical report
PhysicalDescription
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application/pdf
Extent
1 online resource (5 pages)
Note (type = special display note)
Technical report LCSR-TR-252
Name (authority = RutgersOrg-School); (type = corporate)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Name (authority = RutgersOrg-Department); (type = corporate)
NamePart
Computer Science (New Brunswick)
TypeOfResource
Text
TitleInfo
Title
On the frequency of the most frequently occurring variable in dual monotone DNFs
Subject (authority = local)
Topic
Monotone Boolean function
Subject (authority = local)
Topic
Disjunctive normal form
Subject (authority = local)
Topic
Prime implicant
Subject (authority = local)
Topic
Duality
Subject (authority = local)
Topic
Short implicant
Subject (authority = local)
Topic
Frequent variable
Subject (authority = local)
Topic
Transversal hypergraph
Subject (authority = local)
Topic
Clutter
Subject (authority = local)
Topic
Blocker
Subject (authority = local)
Topic
Quasi-polynomial time
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
1995-08
Name (type = personal)
NamePart (type = family)
Gurvich
NamePart (type = given)
Vladimir
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Khachiyan
NamePart (type = given)
Leonid
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
Abstract (type = abstract)
Let f(x1,....., xn) = VIεF^iεIxi and g(x1,.....,xn) = VIεF^iεIxi be a pair of dual monotone irredundant disjunctive normal forms, where F and G are the sets of the prime implicants of f and g, respectively. For a variable xi, i = 1,......, n, let i= #{I ε F|i ε I}/|F| and i = #{I ε G|i ε I}/|G| be the frequencies with which xi occurs in f and g. It is easily seen that maxf{u1, v1,......un,vn}>= 1/ log(|F|+|G|): We give examples of arbitrarily large F and G for which the above bound is tight up to a factor of 2.
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TitleInfo
Title
Computer Science (New Brunswick)
Identifier (type = local)
rucore21032500001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/t3-vzan-q840
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Technical

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Document
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1.4
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GPL Ghostscript 9.07
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:37:24
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:37:24
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