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

## TL;DR

This paper introduces a new inductive rule for verifying lower bounds on expected values and runtimes in probabilistic loops, simplifying the process by avoiding the need to compute limits of sequences.

## Contribution

The paper presents a novel inductive rule that simplifies lower bound verification in probabilistic program analysis by eliminating the need for limit calculations.

## Key findings

- The new rule effectively verifies lower bounds without sequence limits.
- Simplifies probabilistic loop analysis by applying loop body semantics finitely.
- Enhances the efficiency of probabilistic program verification methods.

## 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.