# Weakly synchronous systems with three machines are Turing powerful

arXiv: https://arxiv.org/abs/2308.10578 · HTML: https://mlsanity.com/paper/2308.10578/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 21 Aug 2023.

## Builds on (most cited first, 3 of 3)

- [On the Completeness of Verifying Message Passing Programs under Bounded Asynchrony](https://mlsanity.com/paper/1804.06612/) (2018)
- [Synchronizability of Communicating Finite State Machines is not Decidable](https://mlsanity.com/paper/1702.07213/) (2017)
- [A partial order view of message-passing communication models](https://mlsanity.com/paper/2210.13062/) (2022)

## Abstract (arXiv)

Communicating finite-state machines (CFMs) are a Turing powerful model of asynchronous message-passing distributed systems. In weakly synchronous systems, processes communicate through phases in which messages are first sent and then received, for each process. Such systems enjoy a limited form of synchronization, and for some communication models, this restriction is enough to make the reachability problem decidable. In particular, we explore the intriguing case of p2p (FIFO) communication, for which the reachability problem is known to be undecidable for four processes, but decidable for two. We show that the configuration reachability problem for weakly synchronous systems of three processes is undecidable. This result is heavily inspired by our study on the treewidth of the Message Sequence Charts (MSCs) that might be generated by such systems. In this sense, the main contribution of this work is a weakly synchronous system with three processes that generates MSCs of arbitrarily large treewidth.