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  <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
  "http://www.w3.org/TR/html4/loose.dtd">
  
  <html>
  <head>
  
  <title>
  PRISM Manual | ThePRISMLanguage / CTMCs 
  </title>
  
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      <p><a class='wikilink' href='Main.html'>The PRISM Language</a> /
  </p><h1>CTMCs</h1>
  
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  <!--PageText-->
  <div id='wikitext'>
  <p class='vspace'>Specifying the behaviour of a continuous-time Markov chain (CTMC)
  is done in similar fashion to a DTMC or an MDP, as discussed so far.
  The main difference is that updates in commands are
  labelled with (positive-valued) <em>rates</em>, rather than probabilities.
  The notation used in commands, however, to associate rates to transitions is identical to
  the one used to assign probabilities:
  </p>
  <div class='vspace'></div>
  <div class='sourceblock ' id='sourceblock1'>
    <div class='sourceblocktext'><div class="prism"><span class="prismident">rate_1</span>:<span class="prismident">update_1</span> + <span class="prismident">rate_2</span>:<span class="prismident">update_2</span> + ...<br/>
  </div></div>
    <div class='sourceblocklink'><a href='http://prismmodelchecker.localhost/manual/ThePRISMLanguage/CTMCs?action=sourceblock&amp;num=1' type='text/plain'>[&#036;[Get Code]]</a></div>
  </div>
  
  <p class='vspace'>In a CTMC, when multiple possible transitions are available in a state, a <em>race condition</em> occurs
  (see e.g. [<a class='wikilink' href='../Main/References.html#KNP07a'>KNP07a</a>] for more details).
  In terms of PRISM commands, this can arise in several ways.
  Firstly, within in a module, multiple transitions can be specified either as several different updates in a command, or as multiple commands with overlapping guards. The following, for example. are equivalent:
  </p>
  <div class='vspace'></div>
  <div class='sourceblock ' id='sourceblock2'>
    <div class='sourceblocktext'><div class="prism">[] <span class="prismident">x</span>=<span class="prismnum">0</span> -&gt; <span class="prismnum">50</span>:(<span class="prismident">x</span>'=<span class="prismnum">1</span>) + <span class="prismnum">60</span>:(<span class="prismident">x</span>'=<span class="prismnum">2</span>);<br/>
  </div></div>
    <div class='sourceblocklink'><a href='http://prismmodelchecker.localhost/manual/ThePRISMLanguage/CTMCs?action=sourceblock&amp;num=2' type='text/plain'>[&#036;[Get Code]]</a></div>
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  <div class='sourceblock ' id='sourceblock3'>
    <div class='sourceblocktext'><div class="prism">[] <span class="prismident">x</span>=<span class="prismnum">0</span> -&gt; <span class="prismnum">50</span>:(<span class="prismident">x</span>'=<span class="prismnum">1</span>);<br/>
  [] <span class="prismident">x</span>=<span class="prismnum">0</span> -&gt; <span class="prismnum">60</span>:(<span class="prismident">x</span>'=<span class="prismnum">2</span>);<br/>
  </div></div>
    <div class='sourceblocklink'><a href='http://prismmodelchecker.localhost/manual/ThePRISMLanguage/CTMCs?action=sourceblock&amp;num=3' type='text/plain'>[&#036;[Get Code]]</a></div>
  </div>
  
  <p class='vspace'>Furthermore, parallel composition between modules in a CTMC is modelled as a race condition,
  rather as a nondeterministic choice, like for <a class='wikilink' href='ParallelComposition.html'>MDPs</a>.
  </p>
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