A Demonic Outcome Logic for Randomized Nondeterminism

TL;DR

This paper introduces Demonic Outcome Logic, a new framework for reasoning about programs that combine randomization and nondeterminism, enabling analysis of complex probabilistic behaviors in concurrent and adversarial settings.

Contribution

It presents a novel logic with features for analyzing multiple executions, manipulating conditions with equational laws, and reasoning about loops for termination and outcome distribution.

Findings

Successfully applied to Monty Hall problem

Analyzed adversarial coin simulation protocol

Evaluated probabilistic SAT solver heuristics

Abstract

Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for concurrency, efficiency, or algorithmic design). In this paper, we introduce Demonic Outcome Logic for reasoning about programs that exploit both randomization and nondeterminism. The logic includes several novel features, such as reasoning about multiple executions in tandem and manipulating pre- and postconditions using familiar equational laws -- including the distributive law of probabilistic choices over nondeterministic ones. We also give rules for loops that both establish termination and quantify the distribution of final outcomes from a single premise. We illustrate the reasoning capabilities of Demonic Outcome Logic through several case studies, including the Monty Hall problem, an adversarial protocol for simulating fair coins, and a heuristic based probabilistic SAT solver.