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Counterexample Explanation by Learning Small Strategies in Markov Decision Processes

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BRÁZDIL Tomáš CHATTERJEE Krishnendu CHMELÍK Martin FELLNER Andreas KŘETÍNSKÝ Jan

Druh Článek ve sborníku
Konference Computer Aided Verification: 27th International Conference, CAV 2015
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1007/978-3-319-21690-4_10
Obor Informatika
Klíčová slova stochastic systems; verification; machine learning; decision tree
Popis For deterministic systems, a counterexample to a property can simply be an error trace, whereas 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 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.
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