Automatic Probabilistic Program Verification through Random Variable Abstraction

Damián Barsotti
(Universidad Nacional de Córdoba)
Nicolás Wolovick
(Universidad Nacional de Córdoba)

The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA) and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy.

Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence.

In Alessandra Di Pierro and Gethin Norman: Proceedings Eighth Workshop on Quantitative Aspects of Programming Languages (QAPL 2010), Paphos, Cyprus, 27-28th March 2010 , Electronic Proceedings in Theoretical Computer Science 28, pp. 34–47.
Published: 26th June 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.28.3 bibtex PDF

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