# Automatic Generation of Moment-Based Invariants for Prob-Solvable Loops

## TL;DR

This paper introduces a method to automatically generate moment-based invariants for Prob-Solvable loops in probabilistic programs, enabling comprehensive analysis of loop behaviors beyond expected values.

## Contribution

It presents a novel combination of symbolic summation and statistical methods to derive higher-order moment invariants for a specific class of probabilistic loops.

## Key findings

- Successfully derived invariants for complex probabilistic loops
- Automated computation of higher-order moments demonstrated
- Enhanced analysis capabilities for probabilistic program behaviors

## Abstract

One of the main challenges in the analysis of probabilistic programs is to compute invariant properties that summarise loop behaviours. Automation of invariant generation is still at its infancy and most of the times targets only expected values of the program variables, which is insufficient to recover the full probabilistic program behaviour. We present a method to automatically generate moment-based invariants of a subclass of probabilistic programs, called Prob-Solvable loops, with polynomial assignments over random variables and parametrised distributions. We combine methods from symbolic summation and statistics to derive invariants as valid properties over higher-order moments, such as expected values or variances, of program variables. We successfully evaluated our work on several examples where full automation for computing higher-order moments and invariants over program variables was not yet possible.