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Abstract interpretation of probabilistic semantics
 by David Monniaux.

Abstract
Following earlier models, we lift standard deterministic and nondeterministic semantics of imperative programs to probabilistic semantics. This semantics allows for random external inputs of known or unknown probability and random number generators. We then propose a method of analysis of programs according to this semantics, in the general framework of abstract interpretation. This method lifts an "ordinary" abstract lattice, for non-probabilistic programs, to one suitable for probabilistic programs. Our construction is highly generic. We discuss the in uence of certain parameters on the precision of the analysis, basing ourselves on experimental results.
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