Distribution of Reconfiguration Languages maintaining Tree-like Communication Topology
Daniel Hausmann, Mathieu Lehaut, Nir Piterman
TL;DR
The paper addresses distributing regular trace languages for systems whose communication topology reconfigures during execution, within tree-like architectures. It extends Zielonka’s distributed-automata framework by introducing reconfigurable asynchronous automata (RAA) and a reconfiguration language that jointly reason about computation and evolving architecture. It defines reconfigurable languages via RL-DFA/RL-language formalisms and proves that diamond-closed RL-DFA languages can be distributed by RAAs, using a TDiam-based diamond-closure mechanism over tree-structured topologies. The work generalizes prior quadratic constructions to non-binary, acyclic channel topologies and paves the way for distributed implementations in highly dynamic networks, while highlighting complexity and future directions for broader topologies and reconfiguration primitives.
Abstract
We study how to distribute trace languages in a setting where processes communicate via reconfigurable communication channels. That is, the different processes can connect and disconnect from channels at run time. We restrict attention to communication via tree-like communication architectures. These allow channels to connect more than two processes in a way that maintains an underlying spanning tree and keeps communication continuous on the tree. We make the reconfiguration explicit in the language allowing both a centralized automaton as well as the distributed processes to share relevant information about the current communication configuration. We show that Zielonka's seminal result regarding distribution of regular languages for asynchronous automata can be generalized in this setting, incorporating both reconfiguration and more than binary tree architectures.