From Trees to Tree-Like: Distribution and Synthesis for Asynchronous Automata

2026-01-20

AI Summary

This work addresses the distributed construction and controller synthesis for asynchronous automata under tree-like communication architectures. Building upon Zielonka’s asynchronous automaton model, the authors exploit the local communication properties inherent in tree-like dependence alphabets and their underlying spanning trees to extend a previously known quadratic-time distributed construction method—originally limited to strict tree structures—to the broader class of tree-like architectures. The main contribution lies in achieving an efficient distributed construction for asynchronous automata over such generalized architectures while preserving the original quadratic time complexity. Furthermore, the paper establishes that the distributed controller synthesis problem remains decidable in this setting, with a computational complexity bounded by Tower_d(n).

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Distributed Problem Solving
• 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
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

We revisit constructions for distribution and synthesis of Zielonka's asynchronous automata in restricted settings. We show first a simple, quadratic, distribution construction for asynchronous automata, where the process architecture is tree-like. An architecture is tree-like if there is an underlying spanning tree of the architecture and communications are local on the tree. This quadratic distribution result generalizes the known construction for tree architectures and improves on an older, exponential construction for triangulated dependence alphabets. Lastly we consider the problem of distributed controller synthesis and show that it is decidable for tree-like architectures. This extends the decidability boundary from tree architectures to tree-like keeping the same $\text{Tower}_d(n)$ complexity bound, where $n$ is the size of the system and $d \ge 0$ the depth of the process tree.

Problem

• asynchronous automata
• tree-like architecture
• distributed controller synthesis
• distribution construction
• decidability

Innovation

• asynchronous automata
• tree-like architecture
• quadratic distribution
• distributed controller synthesis
• decidability