Does a Program Yield the Right Distribution? Verifying Probabilistic Programs via Generating Functions

TL;DR

This paper introduces a method for verifying whether probabilistic programs produce a specific distribution by using generating functions, with an automated tool supporting various analysis features.

Contribution

It presents the first decidability result for checking exact output distributions of almost-sure terminating probabilistic programs using generating functions.

Findings

Decidability established for distribution verification in probabilistic programs.

Automated tool 'prodigy' supports invariance checking and compositional reasoning.

Effective analysis of distributions with infinite support demonstrated.

Abstract

We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a program generates exactly a specified distribution over its outputs (provided the program terminates almost surely). The class of distributions that can be specified in our formalism consists of standard distributions (geometric, uniform, etc.) and finite convolutions thereof. Our method relies on representing these (possibly infinite-support) distributions as probability generating functions which admit effective arithmetic operations. We have automated our techniques in a tool called prodigy, which supports automatic invariance checking, compositional reasoning of nested loops, and efficient queries on various quantities of to the output distribution, as demonstrated by experiments.