Aiming Low Is Harder - Inductive Proof Rules for Lower Bounds on Weakest Preexpectations in Probabilistic Program Verification
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We present a new inductive proof rule for reasoning about lower bounds on weakest preexpectations, i.e., expected values of random variables after execution of a probabilistic loop. Our rule is simple in the sense that the semantics of the loop needs to be applied to a candidate lower bound only a finite number of times in order to verify that the candidate is indeed a lower bound. We do not require finding the limit of a sequence as many previous rules did. Furthermore, and also in contrast to existing rules, we do not require the random variables to be bounded.
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