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  <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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  PRISM Manual | ThePRISMLanguage / ParallelComposition 
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      <p><a class='wikilink' href='Main.html'>The PRISM Language</a> /
  </p><h1>Parallel Composition</h1>
  
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  <p>The probabilistic model corresponding to a PRISM language description is constructed as the <em>parallel composition</em> of its modules. In every state of the model, there is a set of commands (belonging to any of the modules) which are enabled, i.e. whose guards are satisfied in that state. The choice between which command is performed (i.e. the <em>scheduling</em>) depends on the model type.
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  <p class='vspace'>For an MDP, as in <a class='wikilink' href='Example1.html'>Example 1</a>, the choice is <em>nondeterministic</em>. By way of example, consider state <code>(0,0)</code> (i.e.  <code>x=0</code> and <code>y=0</code>). There are two commands enabled, one from each module:
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    <div class='sourceblocktext'><div class="prism">[] <span class="prismident">x</span>=<span class="prismnum">0</span> -&gt; <span class="prismnum">0.8</span>:(<span class="prismident">x</span>'=<span class="prismnum">0</span>) + <span class="prismnum">0.2</span>:(<span class="prismident">x</span>'=<span class="prismnum">1</span>);<br/>
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    <div class='sourceblocklink'><a href='http://prismmodelchecker.localhost/manual/ThePRISMLanguage/ParallelComposition?action=sourceblock&amp;num=1' type='text/plain'>[&#036;[Get Code]]</a></div>
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    <div class='sourceblocktext'><div class="prism">[] <span class="prismident">y</span>=<span class="prismnum">0</span> -&gt; <span class="prismnum">0.8</span>:(<span class="prismident">y</span>'=<span class="prismnum">0</span>) + <span class="prismnum">0.2</span>:(<span class="prismident">y</span>'=<span class="prismnum">1</span>);<br/>
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    <div class='sourceblocklink'><a href='http://prismmodelchecker.localhost/manual/ThePRISMLanguage/ParallelComposition?action=sourceblock&amp;num=2' type='text/plain'>[&#036;[Get Code]]</a></div>
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  <p class='vspace'>In state <code>(0,0)</code> of the MDP, there would be a nondeterministic choice between these two probability distributions:
  </p>
  <div class='vspace'></div><ul><li><code>0.8:(0,0) + 0.2:(1,0)</code> (module <code>M1</code> moves)
  </li><li><code>0.8:(0,0) + 0.2:(0,1)</code> (module <code>M2</code> moves)
  </li></ul><p class='vspace'>For a DTMC, the choice is <em>probabilistic</em>: each enabled command is selected with equal probability.
  If <a class='wikilink' href='Example1.html'>Example 1</a> was a DTMC, then in state <code>(0,0)</code> of the model
  the following probability distribution would result:
  </p>
  <div class='vspace'></div><ul><li><code>0.8:(0,0) + 0.1:(1,0) + 0.1:(0,1)</code>
  </li></ul><p class='vspace'>For a <a class='wikilink' href='CTMCs.html'>CTMC</a>, as will be discussed shortly,
  the choice is modelled as a "race" between transitions.
  </p>
  <p class='vspace'>See the later sections on "<a class='wikilink' href='Synchronisation.html'>Synchronisation</a>" and "<a class='wikilink' href='ProcessAlgebraOperators.html'>Process Algebra Operators</a>" for other topics related to parallel composition.
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