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<HTML><HEAD><TITLE>7 Finite Set Constraints: FS</TITLE><LINK href="ozdoc.css" rel="stylesheet" type="text/css"></HEAD><BODY><TABLE align="center" border="0" cellpadding="6" cellspacing="6" class="nav"><TR bgcolor="#DDDDDD"><TD><A href="node28.html#chapter.schedule"><< Prev</A></TD><TD><A href="index.html">- Up -</A></TD><TD><A href="node43.html#chapter.recordc">Next >></A></TD></TR></TABLE><DIV id="chapter.fs"><H1><A name="chapter.fs">7 Finite Set Constraints: <CODE>FS</CODE></A></H1><P>We use the following notation for operations and relations on sets. We write <IMG alt="\cup, \cap" src="latex106.png">, and <IMG alt="\backslash" src="latex107.png"> for set union, intersection, and difference, <IMG alt="\subseteq" src="latex108.png"> and <IMG alt="\|" src="latex109.png"> for inclusion and disjointness, <IMG alt="\#" src="latex110.png"> for the set cardinality, and <IMG alt="\in" src="latex111.png"> for the element relation. Furthermore, we write <IMG alt="\emptyset" src="latex112.png"> and <IMG alt="\uniset" src="latex113.png"> for the empty set and the universal set.</P><P> For every set specification <I>Spec</I> we write the set <I>M</I> specified by <I>Spec</I> as <I>M</I> = <IMG alt="~$
\newcommand{\sic}[2]{\mbox{$[#1,#2]$}}
\newcommand{\conv}{{\it set}}
\newcommand{\convinv}{{\it set}^{-1}}
~$~
\conv({Spec})" src="latex114.png">. For example, <IMG alt="\conv(\mbox{\codeinline{oz}{[1\#3 5 7]}})" src="latex115.png"> denotes <IMG alt="\{1,2,3,5,7\}" src="latex116.png">. Further, for every set <CODE>S</CODE> we denote with <IMG alt="{D} = \convinv({S})" src="latex117.png"> a set description <I>D</I> such that <IMG alt="\conv({\tt D}) = {\tt S}" src="latex118.png">.</P><P>For more information on the finite set constraint system see <A href="bib.html#muellermueller.wlp.97">[MM97]</A>. </P><HR><UL class="toc"><LI><A href="node34.html#section.fs.genral">7.1 Finite Set Intervals</A></LI></UL><UL class="toc"><LI><A href="node35.html#section.fs.integers">7.2 Sets over Integers</A></LI></UL><UL class="toc"><LI><A href="node36.html#section.fs.standard">7.3 Standard Propagators</A></LI></UL><UL class="toc"><LI><A href="node37.html#section.fs.vars">7.4 Finite Set Interval Variables</A><UL class="toc"><LI><A href="node37.html#label364">7.4.1 Declaring a Single Variable</A></LI><LI><A href="node37.html#label373">7.4.2 Declaring a List of Variables</A></LI><LI><A href="node37.html#label382">7.4.3 Declaring a Tuple of Variables</A></LI><LI><A href="node37.html#label391">7.4.4 Declaring a Record of Variables</A></LI></UL></LI></UL><UL class="toc"><LI><A href="node38.html#section.fs.consts">7.5 Finite Set Constants</A></LI></UL><UL class="toc"><LI><A href="node39.html#section.fs.reified">7.6 Reified Propagators</A></LI></UL><UL class="toc"><LI><A href="node40.html#section.fs.iterating">7.7 Iterating and Monitoring</A></LI></UL><UL class="toc"><LI><A href="node41.html#section.fs.reflection">7.8 Reflection</A></LI></UL><UL class="toc"><LI><A href="node42.html#section.fs.distribution">7.9 Distribution</A></LI></UL></DIV><TABLE align="center" border="0" cellpadding="6" cellspacing="6" class="nav"><TR bgcolor="#DDDDDD"><TD><A href="node28.html#chapter.schedule"><< Prev</A></TD><TD><A href="index.html">- Up -</A></TD><TD><A href="node43.html#chapter.recordc">Next >></A></TD></TR></TABLE><HR><ADDRESS><A href="http://www.ps.uni-sb.de/~duchier/">Denys Duchier</A>, <A href="http://www.ps.uni-sb.de/~kornstae/">Leif Kornstaedt</A>, <A href="http://www.ps.uni-sb.de/~homik/">Martin Homik</A>, <A href="http://www.ps.uni-sb.de/~tmueller/">Tobias Müller</A>, <A href="http://www.ps.uni-sb.de/~schulte/">Christian Schulte</A> and <A href="http://www.info.ucl.ac.be/~pvr">Peter Van Roy</A><BR><SPAN class="version">Version 1.4.0 (20110908185330)</SPAN></ADDRESS></BODY></HTML>
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