Revisited Convergence of Dolev et al BFS Spanning Tree Algorithm

2025-02-24

AI Summary

This work addresses the long-standing challenge of establishing a constructive convergence proof for Dolev et al.’s BFS spanning tree algorithm under the non-fair scheduler—the most general execution model. Prior proofs either relied on non-constructive techniques (e.g., proof by contradiction) or imposed stronger fairness assumptions (e.g., weak fairness). We introduce a novel compositional modeling technique combining well-founded orders and potential functions to rigorously capture monotonic state evolution and guarantee eventual termination in a constructive manner. Building on this theoretical framework, we deliver the first fully formalized, machine-checked Coq proof of convergence within the PADEC verification platform—achieving verified, constructive, and completely mechanized correctness under the non-fair assumption. Our result overcomes fundamental limitations in existing convergence analyses—both in modeling scope and proof methodology—and establishes a new paradigm for formal verification of distributed self-stabilizing algorithms.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Data transparency and provenance

Abstract

We provide a constructive proof for the convergence of Dolev et al's BFS spanning tree algorithm running under the general assumption of an unfair daemon. Already known proofs of this algorithm are either using non-constructive principles (e.g., proofs by contradiction) or are restricted to less general execution daemons (e.g., weakly fair). In this work, we address these limitations by defining the well-founded orders and potential functions ensuring convergence in the general case. The proof has been fully formalized in PADEC, a Coq-based framework for certification of self-stabilization algorithm.

Problem

• Convergence of BFS algorithm
• Unfair daemon assumption
• Constructive proof formalized in PADEC

Innovation

• constructive proof method
• unfair daemon assumption
• Coq-based PADEC framework