Proving Termination of Probabilistic Programs Using Patterns

TL;DR

This paper introduces a new algorithm that leverages existing tools to prove almost-sure termination of probabilistic programs by constructing a set of terminating runs with probability one, with applications in probabilistic analysis.

Contribution

It presents a novel algorithm that combines model checking and termination proving tools to establish almost-sure termination of probabilistic programs through pattern refinement.

Findings

Successfully applied to various case studies demonstrating effectiveness.

Can improve lower bounds on reachability probabilities.

Provides a practical approach for probabilistic program verification.

Abstract

Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with probability one ("almost-sure termination"), is an equally important property for randomized algorithms and probabilistic protocols. We suggest a novel algorithm for proving almost-sure termination of probabilistic programs. Our algorithm exploits the power of state-of-the-art model checkers and termination provers for nonprobabilistic programs: it calls such tools within a refinement loop and thereby iteratively constructs a "terminating pattern", which is a set of terminating runs with probability one. We report on various case studies illustrating the effectiveness of our algorithm. As a further application, our algorithm can improve lower bounds on reachability probabilities.