Boolean functions with long prime implicants
Result description
In this short note we introduce a hierarchy of classes of Boolean functions, where each class is defined by the minimum allowed length of prime implicants of the functions in the class. We show that for a given DNF and a given class in the hierarchy, itis possible to test in polynomial time whether the DNF represents a function from the given class. For the first class in the hierarchy we moreover present a polynomial time algorithm which for a given input DNF outputs a shortest logically equivalent DNF, i.e. a shortest DNF representation of the underlying function. This class is therefore a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. For the second class and higher classes in the hierarchy we show that the Boolean minimization problem can be approximated within a constant factor.
Keywords
Set coverConsensus methodDNFBoolean minimizationApproximation algorithmsAnalysis of algorithms
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Boolean functions with long prime implicants
Original language description
In this short note we introduce a hierarchy of classes of Boolean functions, where each class is defined by the minimum allowed length of prime implicants of the functions in the class. We show that for a given DNF and a given class in the hierarchy, itis possible to test in polynomial time whether the DNF represents a function from the given class. For the first class in the hierarchy we moreover present a polynomial time algorithm which for a given input DNF outputs a shortest logically equivalent DNF, i.e. a shortest DNF representation of the underlying function. This class is therefore a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. For the second class and higher classes in the hierarchy we show that the Boolean minimization problem can be approximated within a constant factor.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
GAP202/10/1188: KnowSched: Knowledge Techniques in Scheduling
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Information Processing Letters
ISSN
0020-0190
e-ISSN
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Volume of the periodical
113
Issue of the periodical within the volume
19-21
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
6
Pages from-to
698-703
UT code for WoS article
000325308700002
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
IN - Informatics
Year of implementation
2013