Almost-sure termination of probabilistic algorithms

Establish sound and general proof techniques to prove almost-sure termination of probabilistic algorithms, enabling formal verification without assuming termination a priori. In particular, develop methods applicable to probabilistic programs with random loops and secret-dependent control flow that guarantee termination with probability 1.

Background

The paper’s verification approach assumes the algorithms under consideration always terminate. While this holds for the case studies presented (e.g., Melbourne Shuffle, Oblivious Sampling, Path ORAM, Path Oblivious Heap), termination arguments for broader classes of probabilistic programs remain challenging.

Almost-sure termination—termination with probability 1—is a well-studied property, but the authors note that establishing such termination for some probabilistic algorithms is still unresolved. They reference existing work on proof rules for almost-sure termination, underscoring the need for proof principles that integrate with program logics used to verify obliviousness and independence properties.

References

However, arguing termination of some probabilistic algorithms is still something of an open problem, for algorithms that almost surely terminate.

— Combining Classical and Probabilistic Independence Reasoning to Verify the Security of Oblivious Algorithms (Extended Version)  (2407.00514 - Yan et al., 2024) in Conclusion and Future Work (Section 7)