Probabilistic Program Verification via Inductive Synthesis of Inductive Invariants

TL;DR

This paper introduces an inductive synthesis method for verifying probabilistic programs by generating invariants, effectively bounding outcomes and proving termination, outperforming some existing tools.

Contribution

It presents a novel, source-code level inductive invariant synthesis approach for probabilistic program verification, demonstrating superior performance over current methods.

Findings

Successfully finds invariants for finite and infinite-state programs

Outperforms state-of-the-art probabilistic model checkers

Competitive with modern invariant synthesis tools

Abstract

Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such quantitative reachability properties by generating inductive invariants on source-code level. Our implementation shows promise: It finds invariants for (in)finite-state programs, can beat state-of-the-art probabilistic model checkers, and is competitive with modern tools dedicated to invariant synthesis and expected runtime reasoning.