The Only Undoable CRDTs are Counters

TL;DR

This paper proves that the only CRDTs capable of reliable undo operations are counters, highlighting fundamental limitations in set CRDTs through group theory analysis.

Contribution

It establishes a theoretical limitation showing all undoable CRDTs must be structured as counters, revealing a fundamental trade-off in CRDT design.

Findings

Set CRDTs cannot reliably support undo operations.

Undoable CRDTs are mathematically equivalent to tuples of counters.

Theoretical proof using group theory demonstrates the limitation.

Abstract

In comparing well-known CRDTs representing sets that can grow and shrink, we find caveats. In one, the removal of an element cannot be reliably undone. In another, undesirable states are attainable, such as when an element is present -1 times (and so must be added for the set to become empty). The first lacks a general-purpose undo, while the second acts less like a set and more like a tuple of counters, one per possible element. Using some group theory, we show that this trade-off is unavoidable: every undoable CRDT is a tuple of counters.