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

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.