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<HTML><HEAD><TITLE>5 Finite Domain Constraints: FD</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="node9.html#chapter.search"><< Prev</A></TD><TD><A href="index.html">- Up -</A></TD><TD><A href="node28.html#chapter.schedule">Next >></A></TD></TR></TABLE><DIV id="chapter.fd"><H1><A name="chapter.fd">5 Finite Domain Constraints: <CODE>FD</CODE></A></H1><P>The procedures in this module have the following properties. </P><P>Each of their applications creates a new thread except for basic constraints which may block.</P><P>Most of the propagators perform interval propagation. Only some do domain propagation (i. e. cut holes into domains). </P><P>Equality between variables is exploited, except for some non-linear propagators. For example, <CODE>A<SPAN class="keyword">+</SPAN>A<SPAN class="keyword">=:</SPAN>B</CODE> is equivalent to <CODE>2<SPAN class="keyword">*</SPAN>A<SPAN class="keyword">=:</SPAN>B</CODE> (for notation see sec.infix-ps).</P><P>The constraint store is amplified with constraints <CODE>X<SPAN class="keyword">::</SPAN>Spec</CODE> and equality between variables, e. g., <CODE>X<SPAN class="keyword">=:</SPAN>Y</CODE> is equivalent to <CODE>X=Y</CODE>. </P><P class="margin">relation symbols</P><P> There are generic procedures who take an atomic argument <CODE>A</CODE> to denote an arithmetic relation <IMG alt="\sim_A" src="latex12.png">. The possible atoms and the associated relations are summarized below. </P><TABLE align="center" bgcolor="#f0f0e0"><TR valign="top"><TD><P><CODE>A</CODE></P></TD><TD><P><CODE><SPAN class="string">'=:'</SPAN></CODE> </P></TD><TD><P><CODE><SPAN class="string">'>:'</SPAN></CODE> </P></TD><TD><P><CODE><SPAN class="string">'>=:'</SPAN></CODE> </P></TD><TD><P><CODE><SPAN class="string">'<:'</SPAN></CODE> </P></TD><TD><P><CODE><SPAN class="string">'=<:'</SPAN></CODE> </P></TD><TD><P><CODE><SPAN class="string">'\\=:'</SPAN></CODE></P></TD></TR><TR valign="top"><TD><P><IMG alt="\sim_A" src="latex12.png"> </P></TD><TD><P><IMG alt="=" src="latex13.png"> </P></TD><TD><P><IMG alt=">" src="latex14.png"> </P></TD><TD><P><IMG alt="\geq" src="latex15.png"> </P></TD><TD><P><IMG alt="<" src="latex16.png"> </P></TD><TD><P><IMG alt="\leq" src="latex17.png"> </P></TD><TD><P><IMG alt="\neq" src="latex18.png"></P></TD></TR></TABLE><P> </P><HR><UL class="toc"><LI><A href="node15.html#section.fd.facts">5.1 Some Facts About Propagators</A></LI></UL><UL class="toc"><LI><A href="node16.html#section.fd.condis">5.2 The Concept of Constructive Disjunction</A></LI></UL><UL class="toc"><LI><A href="node17.html#section.fd.general">5.3 Finite Domains</A></LI></UL><UL class="toc"><LI><A href="node18.html#section.fd.telling">5.4 Telling Domains</A></LI></UL><UL class="toc"><LI><A href="node19.html#section.fd.reflection">5.5 Reflection</A></LI></UL><UL class="toc"><LI><A href="node20.html#section.fd.watching">5.6 Watching Domains</A></LI></UL><UL class="toc"><LI><A href="node21.html#section.fd.arithmetic">5.7 Generic Propagators</A></LI></UL><UL class="toc"><LI><A href="node22.html#section.fd.nonlinear">5.8 Symbolic Propagators</A></LI></UL><UL class="toc"><LI><A href="node23.html#section.fd.bool">5.9 0/1 Propagators</A></LI></UL><UL class="toc"><LI><A href="node24.html#section.fd.reified">5.10 Reified Constraints</A></LI></UL><UL class="toc"><LI><A href="node25.html#section.fd.misc">5.11 Miscellaneous Propagators</A></LI></UL><UL class="toc"><LI><A href="node26.html#section.fd.distribution">5.12 Distribution</A></LI></UL><UL class="toc"><LI><A href="node27.html#section.fd.assignment">5.13 Assigning Values</A></LI></UL></DIV><TABLE align="center" border="0" cellpadding="6" cellspacing="6" class="nav"><TR bgcolor="#DDDDDD"><TD><A href="node9.html#chapter.search"><< Prev</A></TD><TD><A href="index.html">- Up -</A></TD><TD><A href="node28.html#chapter.schedule">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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