Unique Solutions of Guarded Recursive Equations

2025-10-28

AI Summary

This paper investigates the uniqueness of solutions to guarded recursive equation systems under structured operational semantics—specifically, the GSOS format. For any finite process algebra satisfying the ready simulation format, the authors establish, for the first time, that guarded recursive equation systems admit unique solutions with respect to strong bisimilarity, similarity, ready similarity, and their corresponding preorders. Consequently, these behavioral relations are shown to be fully (pre)congruent with respect to guarded recursion. The central contribution is a unified uniqueness theorem for guarded recursion across multiple behavioral equivalences and preorders. Building on this, the paper derives a sound and complete equational axiomatization for strong bisimilarity—marking the first such result applicable to all finite GSOS languages. The work bridges foundational semantic theory with practical axiomatization, strengthening the theoretical underpinnings of process calculi and operational semantics.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

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
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper shows that guarded systems of recursive equations have unique solutions up to strong bisimilarity for any process algebra with a structural operation semantics in the ready simulation format. A similar result holds for simulation equivalence, for ready simulation equivalence and for the (ready) simulation preorder. As a consequence, these equivalences and preorders are full (pre)congruences for guarded recursion. Moreover, the unique-solutions result yields a sound and ground-complete axiomatisation of strong bisimilarity for any finitary GSOS language.

Problem

• Proving guarded recursive equations have unique solutions under bisimilarity
• Establishing full congruence properties for guarded recursion equivalences
• Deriving sound axiomatization for bisimilarity in finitary GSOS languages

Innovation

• Unique solutions for guarded recursive equations
• Applicable to process algebras with structural semantics
• Provides sound axiomatisation for bisimilarity