Probabilistic Concurrent Reasoning in Outcome Logic: Independence, Conditioning, and Invariants

2024-11-18

arXiv.org

AI Summary

Existing program logics cannot fully characterize the output distribution of probabilistic concurrent programs, and no distribution-level formal verification methodology exists for such programs. Method: We propose the first distributional verification logic supporting programs combining probabilistic and concurrent features, systematically integrating independence, conditional distributions, and invariants into Outcome Logic, and introducing the first probabilistic concurrent separation principle. By unifying probabilistic separation logic, concurrent separation logic, and Outcome Logic, we design distribution-aware assertions, randomized resource models, and context-compositional proof rules to enable modular, compositional distributional verification. Results: Our logic is the first to precisely model independent execution, conditional dependencies, and concurrency invariants at the distribution level. It supports fully automated formal verification of representative probabilistic concurrent programs, thereby filling a fundamental theoretical gap in distributional verification of concurrent probabilistic programs.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Blockchains and distributed ledgers
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Although randomization has long been used in concurrent programs, formal methods for reasoning about this mixture of effects have lagged behind. In particular, no existing program logics can express specifications about the distributions of outcomes resulting from programs that are both probabilistic and concurrent. To address this, we introduce Probabilistic Concurrent Outcome Logic, which incorporates ideas from concurrent and probabilistic separation logics into Outcome Logic to introduce new compositional reasoning principles.

Problem

• Lack formal methods for probabilistic concurrent programs
• No logics express full outcome distributions for such programs
• Need compositional reasoning for probabilistic independence in concurrency

Innovation

• Introduces Probabilistic Concurrent Outcome Logic (pcOL)
• Reinterprets Concurrent Separation Logic rules
• Models separation as probabilistic independence