Distributed Download from an External Data Source in Asynchronous Faulty Settings

David Peleg; John Augustine; Manish Kumar; Shachar Meir; Soumyottam Chatterjee; Valerie King

REVIEW 1 major objections 5 minor 27 references

Distributed Download from an External Data Source in Asynchronous Faulty Settings

T0 review · 1 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A deterministic protocol solves async download with optimal per-peer query cost

desk verdict First asynchronous treatment of the Data Retrieval model, with a genuinely new crash protocol and a neat randomized Byzantine lower bound, but the main crash result has a proof gap around leftover unknown bits that should be fixed before the optimality claim is trusted. read the letter →

arxiv 2509.03755 v1 pith:7OHCKED4 submitted 2025-09-03 cs.DC

John Augustine , Soumyottam Chatterjee , Valerie King , Manish Kumar , Shachar Meir , David Peleg This is my paper · ORCID

classification cs.DC

keywords distributeddataretrievaldownloadproblemasynchronousnetworkscrashfaultsByzantinequerycomplexityblockchainoraclesdecisiontrees

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether k peers connected by an asynchronous network can jointly learn an n-bit array held by a trusted but expensive external source, when some peers may fail. It answers yes for crash faults: a deterministic protocol lets every nonfaulty peer learn the whole array with O(n/((1−β)k)) expensive lookups to the source, matching the no-failure ideal of n/k up to a constant that depends on the crash fraction, for any fraction β<1. For Byzantine faults the paper draws a line at β=1/2: at or above that fraction, even randomized protocols force some honest peer to query more than n/2 bits, whereas below it a randomized protocol attains near-optimal query complexity. These protocols are also applied to blockchain oracles, reducing the per-node cost of collecting off-chain data from O(mn) to roughly O(mn/k). The headline is the crash result: it shows the "learn everything from the source" task, unlike agreement or broadcast, is deterministically solvable in asynchrony without sacrificing query balance.

What carries the argument

Crash protocol: a sequence of phases, each with an assignment function σ_p mapping every bit of X to the peer responsible for querying it. In stage 1 each peer queries its assigned unknown bits and broadcasts them; in stage 2 each peer waits for k−f replies and reports which peers it has not heard from; in stage 3 the unknown bits of missing peers are redistributed evenly among all peers. Because at most f of the k assignments fail to arrive, the number of bits any peer still lacks is multiplied by at most f/k per phase, and after P=log_{k/f}(n/k) phases the residual is small enough to query directly. Byzantine protocols: parties partition X into segments, each peer broadcasts the segment it

What would settle it

Simulate the crash protocol (Algorithm 2) with concrete parameters, e.g. k=100, f=40, n=1000, run it for P=log_{k/f}(n/k) phases, and count the unknown bits a nonfaulty peer must query in the termination step. Claim 10 predicts roughly n(f/k)^P = k = 100 unknown bits per peer; Lemma 11 requires n/k·(f/k)^P = 1. A direct count decides which bound governs, and thus whether Q is O(n/(γk)) or O(n/(γk)+k).

Watch

Extended reading notes

Core claim

The paper's central claim is a threshold split for the Download problem in asynchronous networks. Under crash faults, it claims a deterministic protocol that solves Download for any f<k crashes with per-peer query complexity Q=O(n/(γk)), where γ=1−f/k, time O(n/ϕ + log_{k/f}(ϕ)), and message complexity O(nk²); because the no-failure load is Θ(n/k), this is optimal up to the 1/γ factor. Under Byzantine faults, it claims that for β≥1/2 every randomized protocol has an execution where some peer queries more than n/2 bits, and every deterministic protocol requires Q=n; for β<1/2 it claims a two-cycle randomized protocol with Q=O(√(n/(γ−β)) + n log n/((γ−β)k)) and a multi-cycle one with expected

Load-bearing premise

The optimal crash protocol's query bound depends on the claim that after the last reassignment phase a peer has only one remaining unknown bit to query; the paper's own phase-by-phase count leaves about k unknown bits per peer at that point, so the strict O(n/(γk)) conclusion needs the geometric decay count to be tightened.

Editorial extensions

If this is right

Any fixed fraction β<1 of crash faults can be tolerated with per-peer query cost O(n/((1−β)k)), the same order as the ideal synchronized no-failure protocol.
Download is solvable deterministically in asynchrony without using reliable broadcast or consensus as a building block, in contrast to classic agreement-style impossibilities.
For Byzantine settings with β≥1/2, randomization cannot reduce the query burden below a constant fraction of n, so the synchronous randomized speedup disappears.
For β<1/2, randomized asynchronous protocols achieve near-optimal expected query complexity, making the synchronous randomized results portable to asynchronous networks.
Blockchain oracle data collection can be load-balanced across peers: the per-node query cost for m data sources drops from O(mn) to roughly O(mn/k), provided the data source is stable across queries.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The strict O(n/(γk)) statement in the crash protocol rests on Lemma 11's claim that the termination phase costs one bit per peer; the paper's own Claim 10 bounds the leftover by k bits per peer at that point, so a charitable reading is Q=O(n/(γk)+k), which is only clearly optimal when n=Ω(k²). That reconciliation is my inference, not the paper's claim.
The f/k geometric-decay template should transfer to other retrieve(f) problems: any function computed locally after downloading X inherits the same per-peer query bound, so the result generalizes beyond the identity function.
The Byzantine β=1/2 threshold suggests a natural test in the barely-minority regime: run the two-cycle protocol with β just below 1/2 and ask whether the √n term is essential or an artifact of the segment-size choice; the paper does not resolve that tradeoff.
The protocol assumes queries to a source return stable, identical values to different peers; if data can change between queries, the reassignment logic breaks, and a plausible necessary condition is snapshot-consistent reads rather than plain read-only access.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First thing to know: this is the first paper to take the Data Retrieval model into the asynchronous setting, and the crash-fault protocol plus the randomized Byzantine lower bound for β ≥ 1/2 are genuinely new. But the query-optimality proof for the main crash protocol has a real gap: Lemma 11 undercounts the leftover unknown bits at termination by a factor of k, so Theorem 12 as written is not established.

The paper does a few things well. The deterministic crash protocol is a natural extension of Algorithm 1 to f crashes, and the geometric decay idea—each phase reduces unknown bits by f/k—is clean. The randomized Byzantine lower bound in Section 3.1 is slick: the adversary delays half the peers and couples an all-zero execution with a one-1 execution; I checked the probability argument and it holds. The Byzantine upper bounds for β < 1/2 are explicitly labeled as adaptations of the authors' own synchronous protocols [3,4], which is honest. The blockchain oracle application is a nice motivation and gives a clear statement of how Download improves per-peer query cost from O(mn) to O(mn/k).

The problem is Lemma 11. Claim 10 says at the start of phase p a peer has at most n(f/k)^p unknown bits. At the termination phase p = log_{k/f}(n/k), that is k bits, not 1 as Lemma 11 uses. The final direct query must cover all remaining unknowns, so you get an additive k, and the query bound becomes O(n/(γk) + k), which is not O(n/(γk)) when n = o(k^2). That is a load-bearing gap for the headline crash result. It is not necessarily fatal: running to log_{k/f}(n) phases leaves one unknown bit and the geometric sum is still O(n/(γk)); the time analysis would need redoing, but the repair looks mechanical. As written though, the optimality claim is unsupported. I did not find a similar issue in the Byzantine sections; those appear sound.

Who is this for: people working on the DR model, distributed retrieval from external sources, or oracle protocols. It is the first asynchronous treatment, so it is a useful reference even if the crash theorem needs a fix. It deserves a serious referee, with a request for a corrected Lemma 11 before the complexity claim is accepted.

Referee Report

1 major / 5 minor

Summary. The paper studies the Distributed Data Retrieval (DR) model in asynchronous networks, focusing on the Download problem: every nonfaulty peer must learn an n-bit array X stored at an external source, while minimizing per-peer queries. The main positive result is a deterministic crash-fault protocol claimed to achieve optimal query complexity Q = O(n/(γk)) for any fraction β < 1 of crashes, with sublinear time and message complexity O(nk^2). For Byzantine faults, the paper proves that when β ≥ 1/2, every randomized asynchronous protocol has an execution in which some peer queries more than n/2 bits, and every deterministic protocol requires Q = n; for β < 1/2, it gives deterministic and randomized protocols with near-optimal query complexity. It also sketches an application to blockchain oracles. The Byzantine lower bounds and randomized protocols are mostly rigorous, but the crash protocol's query-optimality proof contains a concrete off-by-k error in the termination phase.

Significance. If the crash-fault result is repaired, this is a significant contribution: it is the first treatment of the DR model in asynchronous networks, and it shows a separation between crash and Byzantine faults in terms of achievable query complexity. The randomized Byzantine lower bound for β ≥ 1/2 is also notable because it extends the synchronous deterministic lower bound to randomized asynchronous protocols, ruling out randomization as a workaround in the majority-Byzantine regime. The protocols are concrete and the oracle application is a nice practical motivation. However, the central claimed result—deterministic query-optimal Download in the crash model—is not established as written because of a load-bearing error in the query-complexity analysis of Lemma 11, which affects Theorem 12. The paper does not ship machine-checked proofs or code, but the proof structure is otherwise mostly clear and reproducible.

major comments (1)

[Section 2.2, Lemma 11 and Theorem 12] The final additive term in the query bound is wrong. Claim 10 bounds the number of unknown bits per peer at the start of phase p by n·(f/k)^p. The quantity (n/k)·(f/k)^p is therefore the per-phase query cost after uniform reassignment, not the residual unknown-bit count. After P = log_{k/f}(n/k) phases, each nonfaulty peer still has n·(f/k)^P = k unknown bits, so the direct query performed on Line 41 costs k bits, not 1. Hence Lemma 11 supplies Q = O(n/(γk) + k), which is not O(n/(γk)) when n = o(k^2). Since Theorem 12's headline query-optimality claim rests on this bound, it is not established as written. The gap appears repairable, e.g. by running to P = log_{k/f}(n) phases so that the residual is 1 bit, but the time analysis in Lemma 11 would need to be redone; the current text needs revision before the result can be accepted.

minor comments (5)

[Lemma 11 / Theorem 12 statement] The table and contribution list state Q = Θ(n/(γk)), while Theorem 12 only proves an upper bound. If the matching lower bound is not proved or cited, the Θ notation should be replaced by O.
[Theorem 20] In the theorem statement, Q = O(n log n/(γ−βk)) appears to be a typo for Q = O(n log n/((γ−β)k)); the same typo appears in the contributions list.
[Section 3.4 / Algorithm numbering] The text refers to 'Protocol 3' and 'Protocol 4' when the corresponding code blocks are labeled 'Algorithm 3' and 'Algorithm 4'. This is confusing and should be aligned.
[Appendix A] The proof of Theorem 13 defines EX^F_s as a 'synchronous execution' in a paper about asynchronous networks. Since asynchronous executions include synchronous ones, this is formally fine, but it should be stated explicitly to avoid confusion.
[Section 4] The final paragraph correctly notes the restrictive static-data assumption. This limitation is important and should also be stated in the model section, not only in the application section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the load-bearing derivations are in-paper; the self-citations are clearly labeled adaptations rather than inputs to the conclusions.

full rationale

The paper's central crash-fault result (Theorem 12) is derived inside the paper: Claim 10 proves by induction the geometric bound on unknown bits, Lemma 11 sums the per-phase query counts, and Theorem 12 is a direct consequence of the protocol description. The Byzantine lower bounds (Theorems 13 and 14) are proved from indistinguishability arguments in the manuscript. The deterministic Byzantine protocol (Theorem 15) explicitly adapts the synchronous committee protocol of [3], but it supplies its own correctness and complexity proof for the asynchronous setting. The randomized Byzantine protocols (Theorems 17 and 20) describe the decision-tree machinery in Section 3.4.1 and prove the required concentration and induction lemmas (Claim 16, Lemmas 18-19) in the paper, so the companion-paper citation [4] is a labeled source of the technique rather than a black-box premise. No claim is obtained by fitting a parameter to the target quantity, and no equation reduces by construction to an assumed value. The proof of Lemma 11 contains a quantitative inconsistency with Claim 10: Lemma 11's termination-phase cost uses (n/k)(f/k)^P, whereas Claim 10 bounds the remaining unknown bits per peer by n(f/k)^P, which is k at P=log_{k/f}(n/k). This is a real correctness gap in the claimed O(n/(\gamma k)) bound, but it is not a circularity, because the proof does not assume the conclusion it is trying to establish. The self-citations are therefore not load-bearing in a circular sense, and the circularity score is 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

No new entities postulated; the 'cycle' is a modeling device for the asynchronous adversary, not a new physical or mathematical object. The only flexible parameter is message size φ, which is a system-level assumption rather than a fitted constant.

free parameters (1)

message size φ = O(n) (multi-cycle), O(n/γk) (2-cycle), arbitrary (crash protocol)
The protocols assume the system allows messages of size up to φ; the segment size in Protocols 4 and 5 is chosen based on φ, and the query bound depends on this choice. It is a system parameter, not fitted to data.

assumptions (5)

domain assumption The external source is trusted and answers every query correctly; two honest peers querying the same index get the same value, and the value does not change over time.
Explicitly stated in §1.2 and acknowledged as restrictive in §4.
domain assumption The communication network is complete and asynchronous: messages have finite but unbounded delay, and the adversary can delay messages and fail up to βk peers.
Standard asynchronous model, §1.2.
domain assumption For randomized protocols, the adversary can fail a peer only between its local cycles and must set all message latencies for a cycle before the cycle begins.
Defined in §1.2; restricts the adaptivity of the adversary.
standard math Chernoff bounds and union bound arguments hold for probabilistic analysis.
Used in Claims 16 and 18.
standard math The protocol is correct with probability 1 (Las Vegas); failure probability must be 0 for the lower bound contradiction.
Used in the randomized lower bound Theorem 14.

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Cite this review

Pith. "Pith review of Distributed Download from an External Data Source in Asynchronous Faulty Settings." pith.science (2026). https://pith.science/paper/7OHCKED4

@misc{pith2026250903755,
  author       = {Pith},
  title        = {Pith review of: Distributed Download from an External Data Source in Asynchronous Faulty Settings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7OHCKED4}},
  note         = {Machine review of arXiv:2509.03755}
}

abstract

The distributedData Retrieval (DR) model consists of $k$ peers connected by a complete peer-to-peer communication network, and a trusted external data source that stores an array $\textbf{X}$ of $n$ bits ($n \gg k$). Up to $\beta k$ of the peers might fail in any execution (for $\beta \in [0, 1)$). Peers can obtain the information either by inexpensive messages passed among themselves or through expensive queries to the source array $\textbf{X}$. In the DR model, we focus on designing protocols that minimize the number of queries performed by any nonfaulty peer (a measure referred to as query complexity) while maximizing the resilience parameter $\beta$. The Download problem requires each nonfaulty peer to correctly learn the entire array $\textbf{X}$. Earlier work on this problem focused on synchronous communication networks and established several deterministic and randomized upper and lower bounds. Our work is the first to extend the study of distributed data retrieval to asynchronous communication networks. We address the Download problem under both the Byzantine and crash failure models. We present query-optimal deterministic solutions in an asynchronous model that can tolerate any fixed fraction $\beta<1$ of crash faults. In the Byzantine failure model, it is known that deterministic protocols incur a query complexity of $\Omega(n)$ per peer, even under synchrony. We extend this lower bound to randomized protocols in the asynchronous model for $\beta \geq 1/2$, and further show that for $\beta < 1/2$, a randomized protocol exists with near-optimal query complexity. To the best of our knowledge, this is the first work to address the Download problem in asynchronous communication networks.

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Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

Asymptotically optimal validated asynchronous byzantine agreement

Ittai Abraham, Dahlia Malkhi, and Alexander Spiegelman. Asymptotically optimal validated asynchronous byzantine agreement. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing , pages 337--346, 2019

work page 2019

[2] [2]

Astraea: A decentralized blockchain oracle

John Adler, Ryan Berryhill, Andreas Veneris, Zissis Poulos, Neil Veira, and Anastasia Kastania. Astraea: A decentralized blockchain oracle. In 2018 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData) , pag...

work page 2018

[3] [3]

Byzantine Resilient Distributed Computing on External Data

John Augustine, Jeffin Biju, Shachar Meir, David Peleg, Srikkanth Ramachandran, and Aishwarya Thiruvengadam. Byzantine Resilient Distributed Computing on External Data . In Dan Alistarh, editor, 38th International Symposium on Distributed Computing (DISC 2024) , volume 319 of Leibniz International Proceedings in Informatics (LIPIcs) , pages 3:1--3:23, Dag...

work page 2024

[4] [4]

Distributed Download from an External Data Source in Byzantine Majority Settings

John Augustine, Soumyottam Chatterjee, Valerie King, Manish Kumar, Shachar Meir, and David Peleg. Distributed Download from an External Data Source in Byzantine Majority Settings . In DISC , 2025. These proceedings

work page 2025

[5] [5]

Crash-stop failures in asynchronous multiparty session types

Adam D Barwell, Ping Hou, Nobuko Yoshida, and Fangyi Zhou. Crash-stop failures in asynchronous multiparty session types. Logical Methods in Computer Science , 21, 2025

work page 2025

[6] [6]

Another advantage of free choice (extended abstract): Completely asynchronous agreement protocols

Michael Ben-Or. Another advantage of free choice (extended abstract): Completely asynchronous agreement protocols. In Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing , PODC '83, page 27–30, New York, NY, USA, 1983. Association for Computing Machinery

work page 1983

[7] [7]

Another advantage of free choice (extended abstract) completely asynchronous agreement protocols

Michael Ben-Or. Another advantage of free choice (extended abstract) completely asynchronous agreement protocols. In Proceedings of the second annual ACM symposium on Principles of distributed computing , pages 27--30, 1983

work page 1983

[8] [8]

Asynchronous byzantine agreement protocols

Gabriel Bracha. Asynchronous byzantine agreement protocols. Information & Computation , 75:130--143, 1987

work page 1987