Adding Reconfiguration to Zielonka's Asynchronous Automata

TL;DR

This work extends Zielonka's asynchronous automata with reconfigurable communication, allowing processes to dynamically join or leave channels. It proves that reconfigurable and fixed asynchronous automata are expressively equivalent via translations, but fixed representations incur broad information dissemination, which can be costly and undesirable. The authors introduce a formal cost measure separating passive machinery costs from active communication costs, showing regimes where reconfigurability yields lower overall costs, and supply alternative constructions that trade machinery for larger passive costs. They also analyze the structure of switching constructions and discuss implications for privacy and security in distributed systems. Overall, the paper provides a rigorous comparison of fixed versus reconfigurable communication in distributed automata, balancing expressiveness, implementation costs, and practical considerations.

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.

Figures (7)

• Figure 1: An asynchronous automaton $\mathcal{B}$ over three processes $p$, $q$, and $r$. Below each process is the list of letters that contain this process in their domain, and below that is the automaton associated with the process.
• Figure 2: An RAA $\mathcal{A}$ over three processes. The listening function is given to the right of each state.
• Figure 3: On the left, the RAA from Example \ref{['exa:RAA']}. On the right, its translation to an AA.
• Figure 4: Illustration of how the order on the channels in $D$ is maintained. We consider the case where $D=\{1,\ldots,n\}$ and $p_i$ is in charge of channel $i$. The order between the channels is the natural order on $\{1,\ldots, n\}$. The black token indicates the current state for each process. Transitions that are on the same channel are connected with a dashed line. The system is set up for next communication on channel $1$ and all other channels are blocked. Indeed, both processes listening to channel $1$ are ready to interact on $1$ ($p_1$ in state $(1,n+1,D,1)$ and $p_2$ in state $(2,n+1,D,1)$) and for every other channel $i>2$ process $i$ is awaiting communication on $i-1$ ($p_i$ in state $(i,n+1,D,i-1)$) so channel $i$ is not enabled.
• Figure 5: Illustration of how the set $D$ and the switching channel $\mathrm{sc}$ change whenever there is a communication on $\mathrm{sc}$. We consider the case where there are three processes and four channels. Each column corresponds to the status after one more communication on $\mathrm{sc}$. Each channel is in turn the switching channel starting with $4$. The channels in $D$ at a certain time/column are marked with a black box. We cycle through the states in $2^{\{1,\ldots, 4\} \setminus \{\mathrm{sc}\}}$ according to set size first and then lexicographically on the sorted set.

Theorems & Definitions (21)

• Example 2.1
• Example 2.2
• Theorem 3.1
• proof
• Corollary 3.2
• proof
• Theorem 3.3
• proof
• Corollary 3.4
• Theorem 4.1