# Distribution of Behaviour into Parallel Communicating Subsystems

## TL;DR

This paper investigates how complex systems can be decomposed into communicating subsystems while preserving behavioral equivalence, focusing on automata learning and bisimilarity, and proving limitations of such decompositions.

## Contribution

It introduces methods for decomposing systems into communicating subsystems that preserve branching bisimilarity and establishes fundamental limitations of divergence-preserving decompositions.

## Key findings

- Synchronous and asynchronous decompositions maintain branching bisimilarity.
- No universal decomposition operator preserves divergence-preserving branching bisimilarity.
- The study advances understanding of system decomposition in distributed automata learning.

## Abstract

The process of decomposing a complex system into simpler subsystems has been of interest to computer scientists over many decades, for instance, for the field of distributed computing. In this paper, motivated by the desire to distribute the process of active automata learning onto multiple subsystems, we study the equivalence between a system and the total behaviour of its decomposition which comprises subsystems with communication between them. We show synchronously- and asynchronously-communicating decompositions that maintain branching bisimilarity, and we prove that there is no decomposition operator that maintains divergence-preserving branching bisimilarity over all LTSs.