New Approaches for Almost-Sure Termination of Probabilistic Programs

TL;DR

This paper introduces novel methods using supermartingales and the Central Limit Theorem to determine almost-sure termination of probabilistic programs, enabling analysis of cases beyond existing techniques.

Contribution

It presents two new approaches for almost-sure termination analysis, including explicit tail bounds and handling previously unmanageable programs.

Findings

Supermartingales with lower bounds provide sound termination analysis.

The Central Limit Theorem approach can prove termination where other methods fail.

Algorithms for automated analysis of probabilistic program termination.

Abstract

We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.