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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)
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technical report
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application/pdf
Extent
11 p.
Note (type = special display note)
Technical report LCSR-TR-251
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
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)
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
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = approximate)
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
Genre (authority = ExL-Esploro)
Technical Documentation
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Open
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## Technical

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