Oblivious Probabilistic Outcome Logic: Verifying Probabilistic Programs with an Oblivious Adversary

2026-07-17

AI Summary

This work addresses the verification of probabilistic programs featuring nondeterminism controlled by oblivious adversaries—agents that commit to fixed strategies without observing stochastic outcomes. To this end, the paper introduces opOL, a novel logic that, for the first time, formally supports reasoning about such programs. opOL integrates Outcome Logic with Probabilistic Separation Logic, modeling adversarial choices as resources and incorporating constraints for probabilistic independence. This enables compositional reasoning over both probabilistic and nondeterministic branching, as well as proofs of almost-sure termination. The authors mechanize the metatheory of opOL in Lean 4 and demonstrate its expressiveness and practicality through case studies including paging algorithms and leader election protocols.

Abstract

In the context of probabilistic programs, an oblivious adversary resolves nondeterminism without seeing the outcomes of random draws. Obliviousness is a common assumption in online algorithms and distributed protocols, but the complex interaction between random draws and adversarial choices makes it challenging to reason about correctness. While there has been significant progress toward reasoning about programs that combine randomization with nondeterminism, most of the work has focused on the adaptive model, whose omniscient view of program state is too powerful to establish correctness for certain classes of programs. We introduce Oblivious Probabilistic Outcome Logic (opOL), a new logic for reasoning about probabilistic programs with nondeterminism controlled by an oblivious adversary. Building on Outcome Logic and Probabilistic Separation Logic, opOL models adversarial choice as a resource and uses probabilistic independence to ensure that random outcomes are hidden from the adversary. The opOL proof system provides expressive and compositional rules for case analysis on both random and nondeterministic outcomes, and for proving almost-sure termination. Expressivity is tested through several case studies, including a paging algorithm and a leader election protocol. The opOL metatheory and case studies are mechanized in Lean 4.

Problem

• probabilistic programs
• oblivious adversary
• nondeterminism
• formal verification
• randomization

Innovation

• Oblivious Adversary
• Probabilistic Program Verification
• Outcome Logic
• Probabilistic Separation Logic
• Almost-Sure Termination