Aiming Low Is Harder -- Induction for Lower Bounds in Probabilistic Program Verification

Abstract

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to be applied only finitely often in order to verify that the candidates are indeed lower bounds. In particular, it is not necessary to find the limit of a sequence as in many previous rules.

References in corpus (4)

• Aiming Low Is Harder -- Induction for Lower Bounds in Probabilistic Program Verification
• Quantitative Separation Logic - A Logic for Reasoning about Probabilistic Programs
• Lexicographic Ranking Supermartingales: An Efficient Approach to Termination of Probabilistic Programs
• A New Proof Rule for Almost-Sure Termination

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• Expected-Cost Analysis for Probabilistic Programs and Semantics-Level Adaption of Optional Stopping Theorems
• Quantitative Analysis of Assertion Violations in Probabilistic Programs
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• Polar: An Algebraic Analyzer for (Probabilistic) Loops
• Concentration-Bound Analysis for Probabilistic Programs and Probabilistic Recurrence Relations