Probabilistic Program Abstractions

Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of pro- gram abstraction is the relationship between a concrete program, which is difficult to analyze, and an abstraction, which is more tractable. We generalize non-deterministic program abstractions to probabilistic program abstractions by explicitly quantifying the non-deterministic choices made by traditional program abstractions. We upgrade key theoretical program abstraction insights to the probabilistic context. Probabilistic program abstractions provide avenues for utilizing abstraction techniques from the programming languages community to improve the analysis of probabilistic programs.