Abstract-We consider the problem of learning a nondeterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning algorithms that use traditional and a new stochastic state-space partitioning, the latter resulting in the minimum number of states. We then use them to solve the problem of active learning, that uses a knowledgeable teacher to generate samples as counterexamples to simulation equivalence queries. We show that the problem is undecidable in general, but that it becomes decidable under a suitable condition on the teacher which comes naturally from the way samples are generated from failed simulation checks. The latter problem is shown to be undecidable if we impose an additional condition on the learner to always conjecture a minimum state hypothesis. We therefore propose a semi-algorithm using stochastic partitions. Finally, we apply the proposed (semi-) algorithms to infer intermediate assumptions in an automated assume-guarantee verification framework for probabilistic systems.
In REF , L * combined with a stochastic state-space partitioning algorithm makes it possible to learn nondeterministic labeled probabilistic transition systems from tree samples.
Learning Probabilistic Systems from Tree Samples
LICS, pp. 441-450, IEEE, 2012
Computer Science