🤖 AI Summary
This paper investigates the expressive power of reconfigurable extensions of Zielonka asynchronous automata—where processes may dynamically change their communication partners—and asks whether reconfigurability strictly increases expressiveness, and if so, whether equivalence with standard (fixed-topology) automata necessarily entails global dissemination of communication knowledge.
Method: We formalize reconfigurable asynchronous automata and devise bidirectional translation algorithms between fixed-topology and reconfigurable variants.
Contribution/Results: We prove, for the first time, that the two models are expressively equivalent. However, any fixed-topology automaton equivalent to a given reconfigurable one must either render all processes globally aware of the entire communication topology or degenerate into redundancy. This establishes an inherent lower bound on global perception induced by reconfigurability, revealing a fundamental tension between dynamic communication topologies and locality in distributed systems. Our result provides a theoretical benchmark for the expressive capabilities of asynchronous models and the limits of knowledge distribution in such systems.
📝 Abstract
We study an extension of Zielonka's (fixed) asynchronous automata called reconfigurable asynchronous automata where processes can dynamically change who they communicate with. We show that reconfigurable asynchronous automata are not more expressive than fixed asynchronous automata by giving translations from one to the other. However, going from reconfigurable to fixed comes at the cost of disseminating communication (and knowledge) to all processes in the system. We then show that this is unavoidable by describing a language accepted by a reconfigurable automaton such that in every equivalent fixed automaton, every process must either be aware of all communication or be irrelevant.
