A Complete Axiomatization of Branching Bisimilarity for a Simple Process Language with Probabilistic Choice - (Extended Abstract)

2019-11-04

The Art of Modelling Computational Systems

AI Summary

This paper addresses the challenge of axiomatizing behavioral equivalence for process languages featuring both nondeterministic and probabilistic choice. We introduce the first sound and complete equational axiomatization for branching bisimilarity and its rooted variant—rooted branching probabilistic bisimilarity. Our method integrates structural operational semantics with probabilistic concurrency models to construct an equational proof system that supports mechanical verification of probabilistic behavioral equivalence. The key contribution is the first complete characterization of branching bisimulation for a basic, recursion-free process language with probabilistic choice—overcoming a longstanding limitation of classical process algebraic axiomatizations, which traditionally cannot accommodate probabilistic choice. This work bridges the theoretical gap between probabilistic semantics and standard axiomatic methods, thereby establishing a formal foundation for equivalence analysis in probabilistic concurrent systems.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Nonmonotonic 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
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Problem

• Defines branching bisimilarity for probabilistic processes
• Develops equational theory for recursion-free process language
• Proves completeness of axiomatization for bisimilarity

Innovation

• Branching bisimilarity for probabilistic processes
• Equational theory for process language
• Completeness proof using concrete processes