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PRISM Manual | ThePRISMLanguage / Example1
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<p><a class='wikilink' href='Main.html'>The PRISM Language</a> /
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</p><h1>Example 1</h1>
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<p>We will use the following simple example to illustrate the basic concepts of the PRISM language.
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Consider a system comprising two identical processes which must operate under mutual exclusion.
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Each process can be in one of 3 states: {0,1,2}.
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From state 0, a process will move to state 1 with probability 0.2
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and remain in the same state with probability 0.8.
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From state 1, it tries to move to the critical section: state 2.
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This can only occur if the other process is not in its critical section.
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Finally, from state 2, a process will either remain there or move back to state 0
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with equal probability.
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The PRISM code to describe an MDP model of this system can be seen below.
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In the next sections, we explain each aspect of the code in turn.
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</p>
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<div class='vspace'></div>
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<div class='sourceblock ' id='sourceblock1'>
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<div class='sourceblocktext'><div class="prism"><span class="prismcomment">// Example 1</span><br/>
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<span class="prismcomment">// Two process mutual exclusion</span><br/>
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<br/>
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<span class="prismkeyword">mdp</span><br/>
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<br/>
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<span class="prismkeyword">module</span> <span class="prismident">M1</span><br/>
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<br/>
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<span class="prismident">x</span> : [<span class="prismnum">0</span>..<span class="prismnum">2</span>] <span class="prismkeyword">init</span> <span class="prismnum">0</span>;<br/>
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<br/>
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[] <span class="prismident">x</span>=<span class="prismnum">0</span> -> <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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[] <span class="prismident">x</span>=<span class="prismnum">1</span> & <span class="prismident">y</span>!=<span class="prismnum">2</span> -> (<span class="prismident">x</span>'=<span class="prismnum">2</span>);<br/>
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[] <span class="prismident">x</span>=<span class="prismnum">2</span> -> <span class="prismnum">0.5</span>:(<span class="prismident">x</span>'=<span class="prismnum">2</span>) + <span class="prismnum">0.5</span>:(<span class="prismident">x</span>'=<span class="prismnum">0</span>);<br/>
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<br/>
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<span class="prismkeyword">endmodule</span><br/>
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<br/>
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<span class="prismkeyword">module</span> <span class="prismident">M2</span><br/>
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<br/>
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<span class="prismident">y</span> : [<span class="prismnum">0</span>..<span class="prismnum">2</span>] <span class="prismkeyword">init</span> <span class="prismnum">0</span>;<br/>
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<br/>
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[] <span class="prismident">y</span>=<span class="prismnum">0</span> -> <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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[] <span class="prismident">y</span>=<span class="prismnum">1</span> & <span class="prismident">x</span>!=<span class="prismnum">2</span> -> (<span class="prismident">y</span>'=<span class="prismnum">2</span>);<br/>
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[] <span class="prismident">y</span>=<span class="prismnum">2</span> -> <span class="prismnum">0.5</span>:(<span class="prismident">y</span>'=<span class="prismnum">2</span>) + <span class="prismnum">0.5</span>:(<span class="prismident">y</span>'=<span class="prismnum">0</span>);<br/>
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<br/>
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<span class="prismkeyword">endmodule</span><br/>
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</div></div>
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<div class='sourceblocklink'><a href='http://www.prismmodelchecker.org/manual/ThePRISMLanguage/Example1?action=sourceblock&num=1' type='text/plain'>[$[Get Code]]</a></div>
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</div>
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<p class='vspace' style='text-align: center;'><strong>The PRISM Language: Example 1</strong>
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<h3><a class='wikilink' href='../Main/Main.html'>PRISM Manual</a></h3>
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<p><strong><a class='wikilink' href='Main.html'>The PRISM Language</a></strong>
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</p><ul><li><a class='wikilink' href='Main.html'>Introduction</a>
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</li><li><a class='selflink' href='Example1.html'>Example 1</a>
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</li><li><a class='wikilink' href='ModelType.html'>Model Type</a>
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</li><li><a class='wikilink' href='ModulesAndVariables.html'>Modules And Variables</a>
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</li><li><a class='wikilink' href='Commands.html'>Commands</a>
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</li><li><a class='wikilink' href='ParallelComposition.html'>Parallel Composition</a>
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</li><li><a class='wikilink' href='LocalNondeterminism.html'>Local Nondeterminism</a>
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</li><li><a class='wikilink' href='CTMCs.html'>CTMCs</a>
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</li><li><a class='wikilink' href='Example2.html'>Example 2</a>
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</li><li><a class='wikilink' href='Constants.html'>Constants</a>
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</li><li><a class='wikilink' href='Expressions.html'>Expressions</a>
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</li><li><a class='wikilink' href='Synchronisation.html'>Synchronisation</a>
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</li><li><a class='wikilink' href='ModuleRenaming.html'>Module Renaming</a>
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</li><li><a class='wikilink' href='MultipleInitialStates.html'>Multiple Initial States</a>
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</li><li><a class='wikilink' href='GlobalVariables.html'>Global Variables</a>
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</li><li><a class='wikilink' href='CostsAndRewards.html'>Costs And Rewards</a>
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</li><li><a class='wikilink' href='ProcessAlgebraOperators.html'>Process Algebra Operators</a>
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