  While for deterministic systems, a counterexample to a property can simply be
an error trace, counterexamples in probabilistic systems are necessarily more
complex. For instance, a set of erroneous traces with a sufficient cumulative
probability mass can be used. Since these are too large objects to understand
and manipulate, compact representations such as subchains have been considered.
In the case of probabilistic systems with non-determinism, the situation is
even more complex. While a subchain for a given strategy (or scheduler,
resolving non-determinism) is a straightforward choice, we take a different
approach. Instead, we focus on the strategy - which can be a counterexample to
violation of or a witness of satisfaction of a property - itself, and extract
the most important decisions it makes, and present its succinct representation.
The key tools we employ to achieve this are (1) introducing a concept of
importance of a state w.r.t. the strategy, and (2) learning using decision
trees. There are three main consequent advantages of our approach. Firstly, it
exploits the quantitative information on states, stressing the more important
decisions. Secondly, it leads to a greater variability and degree of freedom in
representing the strategies. Thirdly, the representation uses a
self-explanatory data structure. In summary, our approach produces more
succinct and more explainable strategies, as opposed to e.g. binary decision
diagrams. Finally, our experimental results show that we can extract several
rules describing the strategy even for very large systems that do not fit in
memory, and based on the rules explain the erroneous behaviour.
