Probabilistic Program Abstractions

TL;DR

This paper introduces a probabilistic framework for program abstractions, enabling more nuanced reasoning about complex systems by explicitly modeling uncertainty and probabilistic choices within abstracted programs.

Contribution

It generalizes traditional non-deterministic program abstractions to a probabilistic setting, providing new definitions and properties for probabilistic reasoning.

Findings

Framework for probabilistic program abstractions established

Key properties of abstractions extended to probabilistic context

Preliminary ideas for inference on probabilistic abstractions discussed

Abstract

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.