2 research outputs found
Learning Probabilistic Systems from Tree Samples
We consider the problem of learning a non-deterministic 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.Comment: 14 pages, conference paper with full proof
Assume-Guarantee Abstraction Refinement for Probabilistic Systems
We describe an automated technique for assume-guarantee style checking of
strong simulation between a system and a specification, both expressed as
non-deterministic Labeled Probabilistic Transition Systems (LPTSes). We first
characterize counterexamples to strong simulation as "stochastic" trees and
show that simpler structures are insufficient. Then, we use these trees in an
abstraction refinement algorithm that computes the assumptions for
assume-guarantee reasoning as conservative LPTS abstractions of some of the
system components. The abstractions are automatically refined based on tree
counterexamples obtained from failed simulation checks with the remaining
components. We have implemented the algorithms for counterexample generation
and assume-guarantee abstraction refinement and report encouraging results.Comment: 23 pages, conference paper with full proof