Semantic Conflict Model for Collaborative Data Structures

Georgii Semenov; Vitaly Aksenov

arxiv: 2602.19231 · v1 · pith:CGZ2VKR7new · submitted 2026-02-22 · 💻 cs.DC

Semantic Conflict Model for Collaborative Data Structures

Georgii Semenov , Vitaly Aksenov This is my paper

Pith reviewed 2026-05-15 20:49 UTC · model grok-4.3

classification 💻 cs.DC

keywords semantic conflict modelcollaborative data structuresCRDTreplicated journalthree-way mergeconflict resolutionlocal-first systemsLast-Writer-Wins

0 comments

The pith

A semantic conflict model resolves operation conflicts locally by identifying dependencies and rebasing via three-way merge on a replicated journal.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Collaborative systems replicate data so users can edit asynchronously, but concurrent operations create conflicts that must be integrated into one history. Standard CRDTs resolve conflicts implicitly inside the data type, while other techniques often need a central coordinator. This paper defines a conflict model that detects clashes from semantic dependencies between operations. It resolves them by rebasing the conflicting operations onto a reconciling operation through a three-way merge performed over the shared journal. The approach is demonstrated on collaborative registers, giving an explicit version of Last-Writer-Wins and a multi-register entity that supports semi-automatic reconciliation.

Core claim

The paper establishes a conflict model for collaborative data structures in which conflicts are identified by semantic dependencies between operations and resolved by rebasing conflicting operations onto a reconciling operation via a three-way merge over a replicated journal, with explicit formulations provided for a Last-Writer-Wins register and a multi-register entity that enables semi-automatic reconciliation.

What carries the argument

The semantic conflict model, which detects conflicts from semantic dependencies between operations and resolves them by rebasing onto a reconciling operation through three-way merge on a replicated journal.

If this is right

Conflict resolution becomes explicit and visible to users instead of hidden inside opaque CRDT logic.
Reconciliation can proceed entirely locally without any central coordinator.
Standard registers such as Last-Writer-Wins receive an explicit formulation inside the model.
Multi-register entities gain support for semi-automatic reconciliation driven by the same mechanism.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same dependency-plus-rebase pattern could be applied to other replicated structures such as lists or trees once appropriate semantic relations are defined.
The model offers a route to hybrid systems that combine CRDT convergence with selective user-guided merges.
Audit logs of the replicated journal could be used to replay and customize past conflict resolutions.

Load-bearing premise

Semantic dependencies between operations can be identified locally and used to drive conflict resolution without central coordination.

What would settle it

A scenario in which two concurrent operations have a semantic dependency that cannot be determined from local information alone, so the three-way merge on the replicated journal produces an incorrect shared history.

Figures

Figures reproduced from arXiv: 2602.19231 by Georgii Semenov, Vitaly Aksenov.

**Figure 4.** Figure 4: Conflict resolution of 𝑜1 and 𝑜2 with two conflicting premises 𝑜 ′ and 𝑜 ′′ and a conflict resolved concurrently leading to another conflict between 𝑜ˆ1 and 𝑜ˆ2. • Visibility predicate 𝑣𝑖𝑠(𝑎, H𝑟), defining when the effect of an action is visible, so that register is discardcomplete. 3.4 Correctness The presented shared memory model is not strongly convergent, as we expect conflicts to may have indefini… view at source ↗

**Figure 1.** Figure 1: Synchronization algorithm to integrate foreign history H𝑟 ′ into H𝑟 . 𝑜 ′ 𝑜1 𝑜2 ⊢ ∗ ⊢ ∗ ⊢ ≪ ⇒ 𝑜 ′ ✚𝑜1 ✚𝑜2 ⊢ ∗ ⊢ ∗ 𝑜ˆ ⊢ˆ ⊢ˆ ≪ [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: Conflict resolution of 𝑜1 and 𝑜2 with one conflicting premise 𝑜 ′ . 𝑜 ′ 𝑜 ′′ 𝑜1 𝑜2 𝑜3 ⊢ ∗ ⊢ ∗ ⊢ ∗ ⊢ ⊢ ⊢ ≪ ≪ ⇒ 𝑜ˆ 𝑜 ′ 𝑜 ′′ ✚𝑜1 ✚𝑜2 ✚𝑜3 ⊢ ∗ ⊢ ∗ ⊢ ∗ ⊢ˆ ⊢ˆ ⊢ˆ ≪ ⊢ [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Conflict resolution of 𝑜2 against 𝑜1 and 𝑜3 with two conflicting premises 𝑜 ′ and 𝑜 ′′, and the merge operation 𝑜ˆ discarding premise 𝑜 ′ . Then, to define a register 𝑥 = 𝑀𝑖 for our shared memory model, it is sufficient to specify: • Action basis 𝐴𝑖 ; • Interpretation function I : H𝑟 → 𝑆𝑖 mapping local history to the state 𝑠 ∈ 𝑆𝑖 ; • Arbitrary entailment rule, defining premises Γ(𝑎) for each action 𝑎 ∈ 𝐴𝑖 … view at source ↗

**Figure 5.** Figure 5: Conflict resolution on arithmetic register within additive context of 𝑎𝑑𝑑 2, which resulted in 𝑚𝑜𝑣 8. 4.2 Arithmetic Register Let us extend an integer register data type with arithmetic actions𝐴 = {𝑚𝑜𝑣, 𝑎𝑑𝑑,𝑚𝑢𝑙 } with an interpreter I producing the state 𝑠 = (𝜔, 𝜈, 𝛼), where 𝜔 ∈ {=, +, ·} is the current computation mode corresponding to the actions of 𝐴, 𝜈 is the current initial value, and 𝛼 is a sequence … view at source ↗

**Figure 7.** Figure 7: Multi-register example: Alice issues 𝑜𝐴 = [𝑡𝑜𝑢𝑐ℎ 𝑀3, 𝑚𝑜𝑣 𝑀2 1pm-2pm], Bob issues 𝑜𝐵 = [𝑚𝑜𝑣 𝑀3 Meadow’s]. Conflict arises as the effect of 𝑐3 is concurrently discarded by 𝑜𝐵. because, otherwise, the event duration would not have been extended in 𝑜𝐴. These operations are compatible, as they operate on different registers, but they can be simply adjusted, so that the intention conflict and optimistic assumpt… view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper sketches an explicit semantic-dependency model for local-first conflict resolution via three-way merge on a replicated journal, but the claim rests on description alone with no proofs or validation shown.

read the letter

The core idea is to detect semantic dependencies between operations locally, then resolve conflicts by rebasing via three-way merge over a replicated journal instead of relying on implicit CRDT rules or a central coordinator. That framing is distinct from the standard CRDT literature and could matter for designers who want users to see and control merges in collaborative tools. The paper demonstrates it on registers, giving an explicit Last-Writer-Wins formulation and a semi-automatic multi-register case, which shows the model can be applied without changing the underlying replication layer. That part is clean and stays within local-first constraints once the dependencies are known. The main weakness is that the abstract supplies no proofs, no algorithm pseudocode, and no empirical checks, so the central claim that dependencies can be identified and used locally without hidden coordination rests on narrative alone. If the full text adds formal arguments or working code, that would change the picture; right now it does not. This is for people working on collaborative data structures who already know CRDTs and want an alternative that surfaces conflicts explicitly. A reader looking for concrete algorithms or measured performance will come away short. A serious editor should send it to peer review so the authors can supply the missing formalization and checks; the idea is coherent enough to deserve that step even if the current version is thin.

Referee Report

2 major / 1 minor

Summary. The paper introduces a semantic conflict model for collaborative data structures that identifies conflicts via semantic dependencies between operations and resolves them locally by rebasing conflicting operations onto a reconciling operation using a three-way merge over a replicated journal. It demonstrates the model on collaborative registers, including an explicit Last-Writer-Wins formulation and a multi-register entity with semi-automatic reconciliation.

Significance. If the model can be shown to guarantee convergence and local execution without hidden coordination, it would provide a useful explicit alternative to opaque CRDT resolution mechanisms for local-first systems. The register demonstration indicates the approach is at least compatible with simple replicated types, but broader significance hinges on formal verification and extension beyond the presented cases.

major comments (2)

[Abstract] Abstract: the central claim that semantic dependencies can be identified locally to drive rebasing and three-way merge rests entirely on descriptive text; the manuscript supplies no formal definition of the dependency relation, no algorithm for local detection, and no proof of convergence or safety.
[Abstract] Abstract: the demonstration on registers (including the LWW formulation) provides neither detailed pseudocode, machine-checked invariants, nor any empirical evaluation, leaving the practicality and correctness of the semi-automatic multi-register reconciliation unverified.

minor comments (1)

The abstract would benefit from a concise statement of the model's scope (e.g., which data types are supported and which assumptions are required for local dependency identification).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed review and for identifying areas where greater formality and detail would strengthen the presentation of the semantic conflict model. We address each major comment below and commit to revisions that add the requested formal elements without altering the core claims or scope of the work.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that semantic dependencies can be identified locally to drive rebasing and three-way merge rests entirely on descriptive text; the manuscript supplies no formal definition of the dependency relation, no algorithm for local detection, and no proof of convergence or safety.

Authors: We agree that the current version relies on descriptive exposition in Sections 2 and 3. In the revision we will introduce a formal definition of the semantic dependency relation (as a partial order over operation metadata stored in the replicated journal), an explicit local detection algorithm that inspects only locally available operation logs, and a proof sketch establishing convergence and safety under the three-way merge semantics. These additions will appear in a new subsection of Section 3 and will be cross-referenced from the abstract. revision: yes
Referee: [Abstract] Abstract: the demonstration on registers (including the LWW formulation) provides neither detailed pseudocode, machine-checked invariants, nor any empirical evaluation, leaving the practicality and correctness of the semi-automatic multi-register reconciliation unverified.

Authors: The register examples in Section 4 are currently illustrative. We will add detailed pseudocode for the LWW register operations and the multi-register reconciliation procedure, together with machine-checked invariants (expressed in a lightweight TLA+ model) for the core safety properties. Because the paper's primary contribution is the conflict model rather than a performance study, we will not add new empirical benchmarks; instead we will include a brief discussion of implementation considerations and reference existing local-first systems that could serve as evaluation targets. These changes will be placed in an expanded Section 4. revision: partial

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper introduces a semantic conflict model defined directly in terms of identifying conflicts via semantic dependencies between operations and resolving them through rebasing onto a reconciling operation using three-way merge over a replicated journal. This is presented as an independent construction for collaborative data structures, demonstrated on registers including an explicit LWW formulation, without any equations, fitted parameters, self-citations, or uniqueness theorems that reduce the central claims back to their own inputs by construction. The model is scoped to local-first execution and semi-automatic reconciliation without hidden coordination requirements or renamings of prior results.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on domain assumptions about the existence and local identifiability of semantic dependencies and the feasibility of three-way merge reconciliation; no free parameters or new physical entities are introduced.

axioms (2)

domain assumption Operations carry identifiable semantic dependencies that determine when they conflict.
Invoked to enable local conflict detection without central coordination.
domain assumption A three-way merge over a replicated journal can correctly rebase and reconcile conflicting operations.
Core mechanism for explicit resolution stated in the abstract.

pith-pipeline@v0.9.0 · 5415 in / 1158 out tokens · 22288 ms · 2026-05-15T20:49:01.210249+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean; IndisputableMonolith/Cost/FunctionalEquation.lean reality_from_one_distinction; washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

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.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

[1]

Aspnes and M

J. Aspnes and M. Herlihy. 1990. Wait-free data structures in the asyn- chronous PRAM model. InProceedings of the Second Annual ACM Symposium on Parallel Algorithms and Architectures(Island of Crete, Greece)(SPAA ’90). Association for Computing Machinery, New York, NY, USA, 340–349. doi:10.1145/97444.97701

work page doi:10.1145/97444.97701 1990
[2]

Alexandru Baltag and Sonja Smets. 2008. A qualitative theory of dynamic interactive belief revision.Logic and the foundations of game and decision theory (LOFT 7)3 (2008), 9–58

work page 2008
[3]

Carlos Baquero, Paulo Sérgio Almeida, Alcino Cunha, Carla Ferreira, et al. 2017. Composition in state-based replicated data types.Bulletin of EATCS3, 123 (2017)

work page 2017
[4]

C. A. Ellis and S. J. Gibbs. 1989. Concurrency control in groupware systems.SIGMOD Rec.18, 2 (June 1989), 399–407. doi:10.1145/66926. 66963

work page doi:10.1145/66926 1989
[5]

Gowtham Kaki, Swarn Priya, KC Sivaramakrishnan, and Suresh Jagan- nathan. 2019. Mergeable replicated data types.Proc. ACM Program. Lang.3, OOPSLA, Article 154 (Oct. 2019), 29 pages. doi:10.1145/3360580

work page doi:10.1145/3360580 2019
[6]

Martin Kleppmann, Adam Wiggins, Peter van Hardenberg, and Mark McGranaghan. 2019. Local-first software: you own your data, in spite of the cloud. InProceedings of the 2019 ACM SIGPLAN Inter- national Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software(Athens, Greece)(Onward! 2019). As- sociation for Computing Machinery, New ...

work page doi:10.1145/3359591.3359737 2019
[7]

Petr Kuznetsov, Maxence Perion, and Sara Tucci-Piergiovanni

work page
[8]

arXiv:2508.18193 [cs.DC]https://arxiv.org/abs/2508.18193

Wait-free Replicated Data Types and Fair Reconciliation. arXiv:2508.18193 [cs.DC]https://arxiv.org/abs/2508.18193

work page arXiv
[9]

Leslie Lamport. 1978. Time, clocks, and the ordering of events in a distributed system.Commun. ACM21, 7 (July 1978), 558–565. doi:10. 1145/359545.359563

work page arXiv 1978
[10]

T. Mens. 2002. A state-of-the-art survey on software merging.IEEE Transactions on Software Engineering28, 5 (2002), 449–462. doi:10. 1109/TSE.2002.1000449

work page arXiv 2002
[11]

Nuno Preguiça, Marc Shapiro, and Caroline Matheson. 2003. Semantics- Based Reconciliation for Collaborative and Mobile Environments. In On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, Robert Meersman, Zahir Tari, and Douglas C. Schmidt (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 38–55

work page 2003
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Yasushi Saito and Marc Shapiro. 2005. Optimistic replication.ACM Comput. Surv.37, 1 (March 2005), 42–81. doi:10.1145/1057977.1057980

work page doi:10.1145/1057977.1057980 2005
[13]

Kjeld Schmidt and Liam Bannon. 1992. Taking CSCW seriously. Computer Supported Cooperative Work (CSCW)1, 1 (1992), 7–40. doi:10.1007/BF00752449

work page doi:10.1007/bf00752449 1992
[14]

Vitaly Semenov. 2007. Semantics-based Reconciliation of Divergent Replicas in Advanced Concurrent Engineering Environments. InCom- plex Systems Concurrent Engineering, Geilson Loureiro and Richard Curran (Eds.). Springer London, London, 557–564

work page 2007
[15]

2011.A comprehensive study of Convergent and Commutative Repli- cated Data Types

Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski. 2011.A comprehensive study of Convergent and Commutative Repli- cated Data Types. Research Report RR-7506. Inria – Centre Paris- Rocquencourt ; INRIA. 50 pages.https://inria.hal.science/inria- 00555588

work page 2011
[16]

Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski

work page
[17]

InSymposium on Self- Stabilizing Systems

Conflict-free replicated data types. InSymposium on Self- Stabilizing Systems. Springer, 386–400

work page
[18]

Marc Shapiro, Antony Rowstron, and Anne-Marie Kermarrec. 2000. Application-independent reconciliation for nomadic applications. In Proceedings of the 9th Workshop on ACM SIGOPS European Workshop: Beyond the PC: New Challenges for the Operating System(Kolding, Denmark)(EW 9). Association for Computing Machinery, New York, NY, USA, 1–6. doi:10.1145/566726.566728

work page doi:10.1145/566726.566728 2000
[19]

Chengzheng Sun, Xiaohua Jia, Yanchun Zhang, Yun Yang, and David Chen. 1998. Achieving convergence, causality preservation, and in- tention preservation in real-time cooperative editing systems.ACM Trans. Comput.-Hum. Interact.5, 1 (March 1998), 63–108. doi:10.1145/ 274444.274447

work page arXiv 1998
[20]

Robert H. Thomas. 1979. A Majority consensus approach to concur- rency control for multiple copy databases.ACM Trans. Database Syst. 4, 2 (June 1979), 180–209. doi:10.1145/320071.320076

work page doi:10.1145/320071.320076 1979
[21]

Hans Van Ditmarsch, Wiebe van Der Hoek, and Barteld Kooi. 2008. Dynamic epistemic logic. Springer

work page 2008
[22]

Matthew Weidner, Heather Miller, and Christopher Meiklejohn. 2020. Composing and decomposing op-based CRDTs with semidirect prod- ucts.Proc. ACM Program. Lang.4, ICFP, Article 94 (Aug. 2020), 27 pages. doi:10.1145/3408976

work page doi:10.1145/3408976 2020
[23]

W.E. Weihl. 1988. Commutativity-based concurrency control for abstract data types.IEEE Trans. Comput.37, 12 (1988), 1488–1505. doi:10.1109/12.9728 Received xx February 2026; revised xx March 2026; accepted xx April 2026

work page doi:10.1109/12.9728 1988

[1] [1]

Aspnes and M

J. Aspnes and M. Herlihy. 1990. Wait-free data structures in the asyn- chronous PRAM model. InProceedings of the Second Annual ACM Symposium on Parallel Algorithms and Architectures(Island of Crete, Greece)(SPAA ’90). Association for Computing Machinery, New York, NY, USA, 340–349. doi:10.1145/97444.97701

work page doi:10.1145/97444.97701 1990

[2] [2]

Alexandru Baltag and Sonja Smets. 2008. A qualitative theory of dynamic interactive belief revision.Logic and the foundations of game and decision theory (LOFT 7)3 (2008), 9–58

work page 2008

[3] [3]

Carlos Baquero, Paulo Sérgio Almeida, Alcino Cunha, Carla Ferreira, et al. 2017. Composition in state-based replicated data types.Bulletin of EATCS3, 123 (2017)

work page 2017

[4] [4]

C. A. Ellis and S. J. Gibbs. 1989. Concurrency control in groupware systems.SIGMOD Rec.18, 2 (June 1989), 399–407. doi:10.1145/66926. 66963

work page doi:10.1145/66926 1989

[5] [5]

Gowtham Kaki, Swarn Priya, KC Sivaramakrishnan, and Suresh Jagan- nathan. 2019. Mergeable replicated data types.Proc. ACM Program. Lang.3, OOPSLA, Article 154 (Oct. 2019), 29 pages. doi:10.1145/3360580

work page doi:10.1145/3360580 2019

[6] [6]

Martin Kleppmann, Adam Wiggins, Peter van Hardenberg, and Mark McGranaghan. 2019. Local-first software: you own your data, in spite of the cloud. InProceedings of the 2019 ACM SIGPLAN Inter- national Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software(Athens, Greece)(Onward! 2019). As- sociation for Computing Machinery, New ...

work page doi:10.1145/3359591.3359737 2019

[7] [7]

Petr Kuznetsov, Maxence Perion, and Sara Tucci-Piergiovanni

work page

[8] [8]

arXiv:2508.18193 [cs.DC]https://arxiv.org/abs/2508.18193

Wait-free Replicated Data Types and Fair Reconciliation. arXiv:2508.18193 [cs.DC]https://arxiv.org/abs/2508.18193

work page arXiv

[9] [9]

Leslie Lamport. 1978. Time, clocks, and the ordering of events in a distributed system.Commun. ACM21, 7 (July 1978), 558–565. doi:10. 1145/359545.359563

work page arXiv 1978

[10] [10]

T. Mens. 2002. A state-of-the-art survey on software merging.IEEE Transactions on Software Engineering28, 5 (2002), 449–462. doi:10. 1109/TSE.2002.1000449

work page arXiv 2002

[11] [11]

Nuno Preguiça, Marc Shapiro, and Caroline Matheson. 2003. Semantics- Based Reconciliation for Collaborative and Mobile Environments. In On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE, Robert Meersman, Zahir Tari, and Douglas C. Schmidt (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 38–55

work page 2003

[12] [12]

Yasushi Saito and Marc Shapiro. 2005. Optimistic replication.ACM Comput. Surv.37, 1 (March 2005), 42–81. doi:10.1145/1057977.1057980

work page doi:10.1145/1057977.1057980 2005

[13] [13]

Kjeld Schmidt and Liam Bannon. 1992. Taking CSCW seriously. Computer Supported Cooperative Work (CSCW)1, 1 (1992), 7–40. doi:10.1007/BF00752449

work page doi:10.1007/bf00752449 1992

[14] [14]

Vitaly Semenov. 2007. Semantics-based Reconciliation of Divergent Replicas in Advanced Concurrent Engineering Environments. InCom- plex Systems Concurrent Engineering, Geilson Loureiro and Richard Curran (Eds.). Springer London, London, 557–564

work page 2007

[15] [15]

2011.A comprehensive study of Convergent and Commutative Repli- cated Data Types

Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski. 2011.A comprehensive study of Convergent and Commutative Repli- cated Data Types. Research Report RR-7506. Inria – Centre Paris- Rocquencourt ; INRIA. 50 pages.https://inria.hal.science/inria- 00555588

work page 2011

[16] [16]

Marc Shapiro, Nuno Preguiça, Carlos Baquero, and Marek Zawirski

work page

[17] [17]

InSymposium on Self- Stabilizing Systems

Conflict-free replicated data types. InSymposium on Self- Stabilizing Systems. Springer, 386–400

work page

[18] [18]

Marc Shapiro, Antony Rowstron, and Anne-Marie Kermarrec. 2000. Application-independent reconciliation for nomadic applications. In Proceedings of the 9th Workshop on ACM SIGOPS European Workshop: Beyond the PC: New Challenges for the Operating System(Kolding, Denmark)(EW 9). Association for Computing Machinery, New York, NY, USA, 1–6. doi:10.1145/566726.566728

work page doi:10.1145/566726.566728 2000

[19] [19]

Chengzheng Sun, Xiaohua Jia, Yanchun Zhang, Yun Yang, and David Chen. 1998. Achieving convergence, causality preservation, and in- tention preservation in real-time cooperative editing systems.ACM Trans. Comput.-Hum. Interact.5, 1 (March 1998), 63–108. doi:10.1145/ 274444.274447

work page arXiv 1998

[20] [20]

Robert H. Thomas. 1979. A Majority consensus approach to concur- rency control for multiple copy databases.ACM Trans. Database Syst. 4, 2 (June 1979), 180–209. doi:10.1145/320071.320076

work page doi:10.1145/320071.320076 1979

[21] [21]

Hans Van Ditmarsch, Wiebe van Der Hoek, and Barteld Kooi. 2008. Dynamic epistemic logic. Springer

work page 2008

[22] [22]

Matthew Weidner, Heather Miller, and Christopher Meiklejohn. 2020. Composing and decomposing op-based CRDTs with semidirect prod- ucts.Proc. ACM Program. Lang.4, ICFP, Article 94 (Aug. 2020), 27 pages. doi:10.1145/3408976

work page doi:10.1145/3408976 2020

[23] [23]

W.E. Weihl. 1988. Commutativity-based concurrency control for abstract data types.IEEE Trans. Comput.37, 12 (1988), 1488–1505. doi:10.1109/12.9728 Received xx February 2026; revised xx March 2026; accepted xx April 2026

work page doi:10.1109/12.9728 1988