A Zielonka-type Construction for Connectedly Communicating Processes

2026-07-14

AI Summary

This work addresses the synthesis of asynchronous automata from a global deterministic finite-state automaton (DFA) specification in distributed systems where fairness assumptions are relaxed and communication may be intermittent. Focusing on processes exhibiting “connected communication”—meaning that if two processes do not communicate within a bounded delay \(d\), they never communicate again—the paper proposes a generalized Zielonka-style construction. This approach leverages trace-closed regular language theory and integrates the delay parameter \(d\) with the depth of process separation, thereby supporting a broader class of practical architectures, such as client-server models. The resulting asynchronous automata exhibit only polynomial blowup in the number of local states per process relative to the size of the original DFA, with exponential complexity confined to the parameters \(d\) and separation depth.

Abstract

Given a global specification as a trace-closed regular language, Zielonka's theorem provides a construction to synthesise a language equivalent distributed implementation represented as a deterministic asynchronous automaton (AA). The construction is notoriously complicated, which has led to a line of work that considers restrictions on the specifications or on the distributed architectures, with the objective of providing a conceptually simpler construction. A new construction has recently been provided for "fair" specifications, in which all processes participate regularly. In this work, we enhance this construction to enable deterministic finite-state automata (DFA) specifications with "connectedly communicating processes": there should be a constant delay d such that if two processes do not hear from one another after this delay, they will never hear from one another until the end of the run. This is a relaxation of the fairness constraint, in which some process may deliberately stop communicating with another one, e.g. a client-server architecture, where a client stops asking the server for a resource if it did not get any response from it after a while. Our construction results in an AA where every process has a number of local states that is polynomial in the number of states of the DFA, and where the only exponential explosion is related to the parameter d, and the separation depth of processes.

Problem

• distributed synthesis
• asynchronous automata
• connectedly communicating processes
• fairness
• trace-closed specifications

Innovation

• connectedly communicating processes
• Zielonka construction
• asynchronous automata
• distributed synthesis
• trace-closed regular language