Boolean functions with long prime implicants

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F12%3A10126636" target="_blank" >RIV/00216208:11320/12:10126636 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.cs.uic.edu/pub/Isaim2012/WebPreferences/ISAIM2012_Boolean_Cepek_etal.pdf" target="_blank" >http://www.cs.uic.edu/pub/Isaim2012/WebPreferences/ISAIM2012_Boolean_Cepek_etal.pdf</a>

DOI - Digital Object Identifier

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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 class of Boolean functions de?ned by a minimum length of its prime implicants. We show that given a DNF one can test in polynomial time whether it represents a function from this class. Moreover, in case that the answeris af?rmative we present a polynomial time algorithm which outputs a shortest DNF representation of the given function. Therefore the de?ned class of functions is a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. Finally, we present a generalization of the above class which is still recognizable in polynomial time, and for which 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 class of Boolean functions de?ned by a minimum length of its prime implicants. We show that given a DNF one can test in polynomial time whether it represents a function from this class. Moreover, in case that the answeris af?rmative we present a polynomial time algorithm which outputs a shortest DNF representation of the given function. Therefore the de?ned class of functions is a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. Finally, we present a generalization of the above class which is still recognizable in polynomial time, and for which the Boolean minimization problem can be approximated within a constant factor.

Druh

O - Ostatní výsledky

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)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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