Denotational Semantics for Probabilistic and Concurrent Programs

2025-03-04

AI Summary

This work addresses the long-standing challenge of defining a unified denotational semantics for programs exhibiting probabilistic choice, concurrency, and unbounded iteration (e.g., while-loops). Prior approaches handle either concurrency or probability in isolation, but fail to coherently model their interaction under infinite behaviors. We introduce the first compositional semantic model that orthogonally integrates probabilistic branching, conditional execution, iterative loops, and concurrent composition. Our approach builds on pomsets (partially ordered multisets), convex powerdomains, and powerdomain theory, combining testing logic with behavioral sequence modeling. Crucially, it lifts classical pomset and convex language models—previously restricted to bounded behavior—to support infinite computations. The model strictly refines both standard concurrent powerdomains and probabilistic convex powerdomains, ensuring semantic consistency and expressive completeness. As a result, it provides a compositional, mathematically rigorous foundation for reasoning about programs with mixed probabilistic and concurrent effects.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We develop a denotational model for programs that have standard programming constructs such as conditionals and while-loops, as well as probabilistic and concurrent commands. Whereas semantic models for languages with either concurrency or randomization are well studied, their combination is limited to languages with bounded loops. Our work is the first to consider both randomization and concurrency for a language with unbounded looping constructs. The interaction between Boolean tests (arising from the control flow structures), probabilistic actions, and concurrent execution creates challenges in generalizing previous work on pomsets and convex languages, prominent models for those effects, individually. To illustrate the generality of our model, we show that it recovers a typical powerdomain semantics for concurrency, as well as the convex powerset semantics for probabilistic nondeterminism.

Problem

• Develops denotational semantics for probabilistic and concurrent programs.
• Addresses challenges in combining randomization and concurrency with unbounded loops.
• Generalizes previous models for concurrency and probabilistic nondeterminism.

Innovation

• Denotational model for probabilistic concurrent programs
• First to combine randomization and unbounded loops
• Generalizes pomsets and convex languages semantics