Modular Reasoning about Error Bounds for Concurrent Probabilistic Programs

2025-03-06

AI Summary

This paper addresses the challenge of modularly reasoning about error probability bounds in higher-order concurrent probabilistic programs. To this end, it introduces Coneris—the first separation logic supporting such reasoning. Methodologically, it pioneers the concept of “randomized logical atomicity,” extending linearizability to probabilistic semantics by introducing pre-sampled traces and a probabilistic update modality to capture probabilistic state evolution at linearization points. Built upon the Rocq and Iris frameworks, Coneris integrates higher-order separation logic, probabilistic semantic modeling, and formal verification techniques. Its contributions are threefold: (1) the first modular verification framework for error probability bounds of higher-order concurrent probabilistic modules; (2) a fully mechanized metatheory and validation across multiple case studies, including large-scale systems; and (3) rigorous guarantees of correctness and composability for derived error upper bounds.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Logic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

We present Coneris, the first higher-order concurrent separation logic for reasoning about error probability bounds of higher-order concurrent probabilistic programs with higher-order state. To support modular reasoning about concurrent (non-probabilistic) program modules, state-of-the-art program logics internalize the classic notion of linearizability within the logic through the concept of logical atomicity. Coneris extends this idea to probabilistic concurrent program modules. Thus Coneris supports modular reasoning about probabilistic concurrent modules by capturing a novel notion of randomized logical atomicity within the logic. To do so, Coneris utilizes presampling tapes and a novel probabilistic update modality to describe how state is changed probabilistically at linearization points. We demonstrate this approach by means of smaller synthetic examples and larger case studies. All of the presented results, including the meta-theory, have been mechanized in the Rocq proof assistant and the Iris separation logic framework

Problem

• Develops Coneris for error bounds in concurrent probabilistic programs.
• Extends logical atomicity to probabilistic concurrent program modules.
• Uses presampling tapes and probabilistic update modality for state changes.

Innovation

• Higher-order concurrent separation logic
• Randomized logical atomicity concept
• Presampling tapes and probabilistic update modality