Probabilistic affirmation and refutation : Case studies

Elsewhere we have defined counterexamples and independent refutation certificates for conjectures of the form “A is correctly implemented by B”, where A and B are probabilistic programs; and we have implemented a constraint-based tool to generate certificates in the case that the implementation is incorrect. In this paper we extend those results to simple safety properties, and we illustrate the techniques with three case studies. One key contribution is that our techniques are carried out directly at the level of source code. A second key contribution is that we use theoremproving and model-checking techniques together, in complementary ways that have not previously been explored for probabilistic systems.

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