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Semantic Conflict Model for Collaborative Data Structures

Georgii Semenov, Vitaly Aksenov

TL;DR

This paper introduces a conflict model for collaborative data structures that enables explicit, local-first conflict resolution without central coordination and demonstrates the approach on collaborative registers, including an explicit formulation of the Last-Writer-Wins Register and a multi-register entity supporting semi-automatic reconciliation.

Abstract

Digital collaboration systems support asynchronous work over replicated data, where conflicts arise when concurrent operations cannot be unambiguously integrated into a shared history. While Conflict-Free Replicated Data Types (CRDTs) ensure convergence through built-in conflict resolution, this resolution is typically implicit and opaque to users, whereas existing reconciliation techniques often rely on centralized coordination. This paper introduces a conflict model for collaborative data structures that enables explicit, local-first conflict resolution without central coordination. The model identifies conflicts using semantic dependencies between operations and resolves them by rebasing conflicting operations onto a reconciling operation via a three-way merge over a replicated journal. We demonstrate our approach on collaborative registers, including an explicit formulation of the Last-Writer-Wins Register and a multi-register entity supporting semi-automatic reconciliation.

Semantic Conflict Model for Collaborative Data Structures

TL;DR

This paper introduces a conflict model for collaborative data structures that enables explicit, local-first conflict resolution without central coordination and demonstrates the approach on collaborative registers, including an explicit formulation of the Last-Writer-Wins Register and a multi-register entity supporting semi-automatic reconciliation.

Abstract

Digital collaboration systems support asynchronous work over replicated data, where conflicts arise when concurrent operations cannot be unambiguously integrated into a shared history. While Conflict-Free Replicated Data Types (CRDTs) ensure convergence through built-in conflict resolution, this resolution is typically implicit and opaque to users, whereas existing reconciliation techniques often rely on centralized coordination. This paper introduces a conflict model for collaborative data structures that enables explicit, local-first conflict resolution without central coordination. The model identifies conflicts using semantic dependencies between operations and resolves them by rebasing conflicting operations onto a reconciling operation via a three-way merge over a replicated journal. We demonstrate our approach on collaborative registers, including an explicit formulation of the Last-Writer-Wins Register and a multi-register entity supporting semi-automatic reconciliation.
Paper Structure (14 sections, 2 theorems, 2 equations, 7 figures)

This paper contains 14 sections, 2 theorems, 2 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Conflict Model
  4. Conflict Identification
  5. Conflict Resolution
  6. Register Definition
  7. Correctness
  8. Examples
  9. Register
  10. Arithmetic Register
  11. LWW-Register
  12. Multi-Register
  13. Related work
  14. Conclusion

Key Result

theorem 1

A graph data type, equivalent to the entailment graph $G_{\vdash}$, which supports operations $add(\Gamma, o)$ (adding a new vertex $o$ with its incoming edges $\Gamma$) and $rebase(o, \hat{o})$ (adding an edge to $o$ from $\hat{o}$ not succeeding it) satisfies SEC Shapiro2011SSSS, i.e., all replica

Figures (7)

  • Figure 1: Synchronization algorithm to integrate foreign history $\mathcal{H}_{r'}$ into $\mathcal{H}_{r}$.
  • Figure 2: Conflict resolution of $o_1$ and $o_2$ with one conflicting premise $o'$.
  • Figure 3: Conflict resolution of $o_2$ against $o_1$ and $o_3$ with two conflicting premises $o'$ and $o"$, and the merge operation $\hat{o}$ discarding premise $o'$.
  • Figure 4: Conflict resolution of $o_1$ and $o_2$ with two conflicting premises $o'$ and $o"$ and a conflict resolved concurrently leading to another conflict between $\hat{o}_1$ and $\hat{o}_2$.
  • Figure 5: Conflict resolution on arithmetic register within additive context of $add \ 2$, which resulted in $mov \ 8$.
  • ...and 2 more figures

Theorems & Definitions (3)

  • definition 1
  • theorem 1
  • theorem 2