Staff View
On Generating the Irredundant Conjunctive And Disjunctive Normal Forms Of Monotone Boolean Functions

Descriptive

Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = RULIB-FS)
Other
Genre (authority = marcgt)
technical report
PhysicalDescription
InternetMediaType
application/pdf
Extent
11 p.
Note (type = special display note)
Technical report LCSR-TR-251
Name (type = corporate); (authority = RutgersOrg-School)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Name (type = corporate); (authority = RutgersOrg-Department)
NamePart
Computer Science (New Brunswick)
TypeOfResource
Text
Abstract (type = abstract)
Let f:{0,1}n→{0,1} be a monotone Boolean function whose value at any point x∈{0,1}n can be determined in time t. Denote by the irredundant CNF of f, where C is the set of the prime implicates of f. Similarly, let be the irredundant DNF of the same function, where D is the set of the prime implicants of f. We show that given subsets C′⊆C and D′⊆D such that (C′,D′)≠(C,D), a new term in (C⧹C′)∪(D⧹D′) can be found in time , where m=|C′|+|D′|. In particular, if f(x) can be evaluated for every x∈{0,1}n in polynomial time, then the forms c and d can be jointly generated in incremental quasi-polynomial time. On the other hand, even for the class of ∧,∨-formulae f of depth 2, i.e., for CNFs or DNFs, it is unlikely that uniform sampling from within the set of the prime implicates and implicants of f can be carried out in time bounded by a quasi-polynomial 2polylog(·) in the input size of f. We also show that for some classes of polynomial-time computable monotone Boolean functions it is NP-hard to test either of the conditions D′=D or C′=C. This provides evidence that for each of these classes neither conjunctive nor disjunctive irredundant normal forms can be generated in total (or incremental) quasi-polynomial time. Such classes of monotone Boolean functions naturally arise in game theory, networks and relay contact circuits, convex programming, and include a subset of ∧,∨-formulae of depth 3.
Name (type = personal)
NamePart (type = family)
Gurvich
NamePart (type = given)
Vladimir
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (type = text); (authority = marcrt)
author
Name (type = personal)
NamePart (type = family)
Khachiyan
NamePart (type = given)
Leonid
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (type = text); (authority = marcrt)
author
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = approximate); (keyDate = yes)
1995
TitleInfo
Title
On Generating the Irredundant Conjunctive And Disjunctive Normal Forms Of Monotone Boolean Functions
RelatedItem (type = host)
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/T3Z89GWD
Back to the top

Rights

RightsDeclaration (AUTHORITY = rightsstatements.org); (TYPE = IN COPYRIGHT); (ID = http://rightsstatements.org/vocab/InC/1.0/)
This Item is protected by copyright and/or related rights.You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use.For other uses you need to obtain permission from the rights-holder(s).
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
Back to the top

Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
Document
CreatingApplication
Version
1.4
ApplicationName
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
Back to the top
Version 8.3.13
Rutgers University Libraries - Copyright ©2020