# Computing Expected Runtimes for Constant Probability Programs

## TL;DR

This paper introduces constant probability programs, providing a decision procedure for their almost sure termination and an algorithm to compute their exact expected runtimes efficiently.

## Contribution

It defines CP programs and offers a novel, straightforward method to determine their termination behavior and expected runtime, extending classical probability theory results.

## Key findings

- Decidable almost sure termination for CP programs
- Efficient computation of expected runtimes for CP programs
- Asymptotically tight bounds on expected runtimes

## Abstract

We introduce the class of constant probability (CP) programs and show that classical results from probability theory directly yield a simple decision procedure for (positive) almost sure termination of programs in this class. Moreover, asymptotically tight bounds on their expected runtime can always be computed easily. Based on this, we present an algorithm to infer the exact expected runtime of any CP program.