The PRISM Language /

Partially Observable Models

PRISM supports analysis of partially observable probabilistic models, most notably partially observable Markov decision processes (POMDPs), but also partially observable probabilistic timed automata (POPTAs). POMDPs are a variant of MDPs in which the strategy/policy which resolves nondeterministic choices in the model is unable to see the precise state of the model, but instead just observations of it. For background material on POMDPs and POPTAs, see for example [NPZ17]. You can also find several example models included in the PRISM distribution. Look in the prism-examples/pomdps and prism-examples/poptas directories.

PRISM currently supports state-based observations: this means that, upon entering a new POMDP state, the observation is determined by that state. In the same way that a model state comprises the values or one or more variables, an observation comprises one or more observables. There are several way to define these observables. The simplest is to specify a subset of the model's variables that are designated as being observable. The rest are unobservable.

For example, in a POMDP with 3 variables, s, l and h, the following:

observables s, l endobservables

specifies that s and l are observable and h is not.

Alternatively, observables can be specified as arbitrary expressions over variables. For example, assuming the same variables s, l and h, this specification:

observable "s" = s;
observable "pos" = l>0;

defines 2 observables. The first is, as above, the variable s. The second, named "pos", determines if variable l is positive. Other than this, the values of l and h are unobservable. The named observables can then be used in properties in the same way that labels can.

The above two styles of definition can also be mixed to specify a combined set of observables.

POPTAs (partially observable PTAs) combine the features of both PTAs and POMDPs. They are are currently analysed using the digital clocks engine, so inherit the restrictions for that engine. Furthermore, for a POPTA, all clock variables must be observable.

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