Boolean functions with long prime implicants

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10144055" target="_blank" >RIV/00216208:11320/13:10144055 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.ipl.2013.07.001" target="_blank" >http://dx.doi.org/10.1016/j.ipl.2013.07.001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ipl.2013.07.001" target="_blank" >10.1016/j.ipl.2013.07.001</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Boolean functions with long prime implicants

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Boolean functions with long prime implicants

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP202%2F10%2F1188" target="_blank" >GAP202/10/1188: KnowSched: Znalostní techniky v rozvrhování</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Information Processing Letters

ISSN

0020-0190

e-ISSN

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Svazek periodika

113

Číslo periodika v rámci svazku

19-21

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

698-703

Kód UT WoS článku

000325308700002

EID výsledku v databázi Scopus

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