03B05-DNF.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{DNF}
\pmcreated{2013-03-22 14:14:08}
\pmmodified{2013-03-22 14:14:08}
\pmowner{rspuzio}{6075}
\pmmodifier{rspuzio}{6075}
\pmtitle{DNF}
\pmrecord{4}{35677}
\pmprivacy{1}
\pmauthor{rspuzio}{6075}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{03B05}
\pmsynonym{disjunctive normal form}{DNF}
\pmrelated{CNF}
\pmrelated{AtomicFormula}

\endmetadata

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%\usepackage{psfrag}
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%\usepackage{graphicx}
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\begin{document}
A propositional formula is a DNF formula, meaning Disjunctive Normal Form, if it is a disjunction of conjunctions of literals (a literal is a propositional variable or its negation). Hence, a DNF is a formula of the form: $K_1 \vee K_2 \vee \ldots \vee K_n$, where each $K_i$ is of the form $l_{i1} \wedge l_{i2} \wedge \ldots \wedge l_{im}$ for literals $l_{ij}$ and some $m$ which can vary for each $K_i$.

Example: $(x\wedge  y \wedge \neg z) \vee (y\wedge \neg w \wedge \neg u) \vee (x \wedge v)$.
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