Wait-Only Broadcast Protocols are Easier to Verify

2025-06-27

AI Summary

This paper investigates two fundamental verification problems—synchronizability (i.e., existence of an execution reaching a target state in all processes) and recurrent coverability (i.e., existence of an infinite execution triggering a given transition infinitely often)—for wait-only (stateless, simultaneous send/receive) finite-state protocols under broadcast communication in parameterized systems. Since both problems are undecidable for general protocols, we introduce the wait-only model and develop a parameterized verification framework grounded in automata-theoretic analysis and complexity-theoretic reductions. Our results establish that synchronizability is Ackermann-complete—yielding the first precise complexity characterization—and reduce the upper bound for recurrent coverability to EXPSPACE, while proving a matching PSPACE-hard lower bound. This work provides the first theoretically rigorous and algorithmically feasible solution for infinite-state verification of broadcast-based concurrent systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Agent Communication
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study networks of processes that all execute the same finite-state protocol and communicate via broadcasts. We are interested in two problems with a parameterized number of processes: the synchronization problem which asks whether there is an execution which puts all processes on a given state; and the repeated coverability problem which asks if there is an infinite execution where a given transition is taken infinitely often. Since both problems are undecidable in the general case, we investigate those problems when the protocol is Wait-Only, i.e., it has no state from which a process can both broadcast and receive messages. We establish that the synchronization problem becomes Ackermann-complete, and the repeated coverability problem is in EXPSPACE, and PSPACE-hard.

Problem

• Verifying synchronization in Wait-Only broadcast protocols
• Analyzing repeated coverability in finite-state broadcast networks
• Determining complexity for parameterized process synchronization

Innovation

• Wait-Only protocols simplify verification
• Synchronization problem is Ackermann-complete
• Repeated coverability in EXPSPACE