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PRISM Manual | ThePRISMLanguage / PartiallyObservableModels
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<p><a class='wikilink' href='Main.html'>The PRISM Language</a> /
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</p><h1>Partially Observable Models</h1>
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<div id='wikitext'>
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<p>PRISM supports analysis of <em>partially observable</em> probabilistic models,
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most notably partially observable Markov decision processes (POMDPs),
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but also partially observable probabilistic timed automata (POPTAs).
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POMDPs are a variant of MDPs in which the strategy/policy/adversary
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which resolves nondeterministic choices in the model is unable to
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see the precise state of the model, but instead just <em>observations</em> of it.
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For background material on POMDPs and POPTAs, see for example [<a class='wikilink' href='../Main/References.html#NPZ17'>NPZ17</a>].
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You can also find several example models included in the PRISM distribution.
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Look in the <code>prism-examples/pomdps</code> and <code>prism-examples/poptas</code> directories.
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</p>
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<p class='vspace'>PRISM currently supports state-based observations:
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this means that, upon entering a new POMDP state,
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the observation is determined by that state.
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In the same way that a model state comprises the values or one or more variables,
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an observation comprises one or more <em>observables</em>.
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There are several way to define these observables.
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The simplest is to specify a subset of the model's variables
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that are designated as being observable. The rest are unobservable.
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</p>
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<p class='vspace'>For example, in a POMDP with 3 variables, <code>s</code>, <code>l</code> and <code>h</code>, the following:
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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="prismkeyword">observables</span> <span class="prismident">s</span>, <span class="prismident">l</span> <span class="prismkeyword">endobservables</span> <br/>
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</div></div>
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<div class='sourceblocklink'><a href='http://www.prismmodelchecker.org/manual/ThePRISMLanguage/PartiallyObservableModels?action=sourceblock&num=1' type='text/plain'>[$[Get Code]]</a></div>
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</div>
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<p class='vspace'>specifies that <code>s</code> and <code>l</code> are observable and <code>h</code> is not.
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</p>
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<p class='vspace'>Alternatively, observables can be specified as arbitrary expressions over variables.
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For example, assuming the same variables <code>s</code>, <code>l</code> and <code>h</code>, this specification:
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<div class='sourceblocktext'><div class="prism"><span class="prismkeyword">observable</span> "<span class="prismident">s</span>" = <span class="prismident">s</span>;<br/>
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<span class="prismkeyword">observable</span> "<span class="prismident">pos</span>" = <span class="prismident">l</span>><span class="prismnum">0</span>;<br/>
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</div></div>
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<div class='sourceblocklink'><a href='http://www.prismmodelchecker.org/manual/ThePRISMLanguage/PartiallyObservableModels?action=sourceblock&num=2' type='text/plain'>[$[Get Code]]</a></div>
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</div>
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<p class='vspace'>defines 2 observables. The first is, as above, the variable <code>s</code>.
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The second, named <code>"pos"</code>, determines if variable <code>l</code> is positive.
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Other than this, the values of <code>l</code> and <code>h</code> are unobservable.
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The named observables can then be used in properties
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in the same way that <a class='wikilink' href='FormulasAndLabels.html'>labels</a> can.
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</p>
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<p class='vspace'>The above two styles of definition can also be mixed
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to specify a combined set of observables.
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</p>
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<p class='vspace'>POPTAs (partially observable PTAs) combine the features of both PTAs and POMDPs.
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They are are currently analysed using the digital clocks engine,
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so inherit the <a class='wikilink' href='Real-timeModels.html'>restrictions for that engine</a>.
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Furthermore, for a POPTA, all clock variables must be observable.
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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='wikilink' 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='FormulasAndLabels.html'>Formulas And Labels</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='Real-timeModels.html'>Real-time Models</a>
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</li><li><a class='selflink' href='PartiallyObservableModels.html'>Partially Observable Models</a>
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</li><li><a class='wikilink' href='ProcessAlgebraOperators.html'>Process Algebra Operators</a>
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</li><li><a class='wikilink' href='PRISMModelFiles.html'>PRISM Model Files</a>
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</li></ul><p>[ <a class='wikilink' href='AllOnOnePage.html'>View all</a> ]
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