On Parameterized Verification Over Tree Topologies

2026-06-25

AI Summary

This study addresses the parameterized safety verification problem for finite-state processes with rendezvous synchronization under tree-shaped topologies—a setting where the problem is known to be undecidable for linear topologies. The authors introduce, for the first time in the context of tree structures, phase-bounded constraints that limit the number of alternations between upward and downward synchronizations, and combine them with depth-bounded conditions to systematically analyze verification complexity under both restrictions. Leveraging parameterized modeling, tree-topology analysis, and fast-growing hierarchy theory, they establish that verification is EXPSPACE-complete when the number of phases is fixed, 2EXPSPACE-complete when the phase bound is part of the input, and precisely characterized by the fast-growing hierarchy under depth-boundedness. This work reveals the fundamental impact of synchronization structure in tree topologies on verification complexity.

Abstract

Parameterized verification of finite-state processes with rendez-vous synchronization is notoriously undecidable when processes are linearly ordered. In this paper we study two kinds of bounds under which we determine the complexity of safety checking over tree topologies. When bounding the depth we obtain that the complexity is related to the fast growing hierarchy. Our second bound limits the alternations between upwards and downwards synchronizations in the tree (phases), and occurs naturally in many concrete settings. If we fix the number of phases then the complexity of safety checking is EXPSPACE complete, and if the number of phases is part of the input it is 2EXPSPACE complete (both for arbitrary depth).

Problem

• parameterized verification
• tree topologies
• rendez-vous synchronization
• safety checking
• phase alternations

Innovation

• parameterized verification
• tree topologies
• rendez-vous synchronization
• phase-bounded
• fast growing hierarchy