Probabilistic Program Abstractions
This work addresses the lack of probabilistic program abstractions for reasoning about complex systems, but it appears incremental as it builds on existing non-deterministic methods.
The authors tackled the problem of generalizing non-deterministic program abstractions to probabilistic ones by quantifying non-deterministic choices, resulting in a framework that upgrades key definitions and properties to the probabilistic context.
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 program abstraction is the relationship between a concrete program, which is difficult to analyze, and an abstract program, which is more tractable. Program abstractions, however, are typically not probabilistic. We generalize non-deterministic program abstractions to probabilistic program abstractions by explicitly quantifying the non-deterministic choices. Our framework upgrades key definitions and properties of abstractions to the probabilistic context. We also discuss preliminary ideas for performing inference on probabilistic abstractions and general probabilistic programs.