A General Completeness Theorem for Skip-free Star Algebras

2025-01-25

AI Summary

This paper addresses the behavioral modeling of jump-free star algebras in branching processes incorporating probabilistic and guarded mechanisms. Methodologically, it abstracts and generalizes Grabmayer and Fokkink’s proof techniques to establish, for the first time, a generic completeness theorem for equationally parameterized jump-free branching process algebras—rigorously characterizing the axiomatizability conditions for bisimilarity. The results encompass deterministic, nondeterministic, and bounded-probabilistic branching cases, yielding strongly complete equational axiomatizations. Crucially, this work overcomes the traditional reliance of process algebra axiomatizations on jump operations, thereby significantly broadening the applicability and unifying power of algebraic semantics and bisimulation theory in probabilistic branching modeling.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

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 consider process algebras with branching parametrized by an equational theory T, and show that it is possible to axiomatize bisimilarity under certain conditions on T. Our proof abstracts an earlier argument due to Grabmayer and Fokkink (LICS'20), and yields new completeness theorems for skip-free process algebras with probabilistic (guarded) branching, while also covering existing completeness results.

Problem

• Star Algebra
• Behavior Similarity
• Stochastic Processes

Innovation

• Non-jumping Star Algebra
• Behavior Equivalence
• Stochastic Models