pith. sign in

arxiv: 2606.17860 · v1 · pith:ZT2KWHCYnew · submitted 2026-06-16 · 💻 cs.DC · cs.LO

An Epistemic Analysis of Random Coordinated Attack

Sophia Knight , David Lehnherr , Sergio Rajsbaum This is my paper

Pith reviewed 2026-06-26 22:48 UTC · model grok-4.3

classification 💻 cs.DC cs.LO
keywords epistemic logicrandomized algorithmscoordinated attackdynamic networksindistinguishabilitycommon knowledgeVarghese-Lynch algorithmprobabilistic knowledge
0
0 comments X

The pith

An epistemic logic framework for bounded-round randomized algorithms shows the Varghese-Lynch coordinated attack solution meets a tight lower bound via indistinguishability.

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

The coordinated attack problem asks whether processes can agree on a joint action within a time bound when messages may be lost. The deterministic version is impossible, but a randomized version using coin flips is solvable. The paper introduces a probabilistic epistemic logic that models knowledge, indistinguishability, and task solvability for randomized algorithms running a fixed number of rounds in dynamic networks under an adversary. It applies the framework to the Varghese-Lynch algorithm, giving a knowledge-theoretic account of its execution and proving that its lower bound is tight. The analysis demonstrates that epistemic reasoning about what processes know remains necessary even when randomness is present.

Core claim

The authors develop a probabilistic epistemic logic framework that characterizes solvability for randomized tasks such as coordinated attack in synchronous dynamic graphs where an adversary controls message loss. Applying the framework to the Varghese-Lynch algorithm yields a formal treatment of the algorithm together with a strengthened lower bound that is shown to be tight; the proof proceeds by indistinguishability arguments, and the information level defined by Varghese and Lynch is shown to correspond to a particular epistemic formula.

What carries the argument

The probabilistic epistemic logic framework that combines dynamic-network task characterization with probabilistic dynamic epistemic logic to define probabilistic epistemic task solvability.

If this is right

  • Knowledge-theoretic reasoning remains necessary to prove lower bounds for randomized distributed tasks.
  • The information level used by Varghese and Lynch equals a specific epistemic formula expressible in the new logic.
  • The same framework applies directly to randomized versions of approximate agreement and consensus in dynamic networks.
  • Indistinguishability arguments continue to separate solvable from unsolvable randomized tasks even after coin flips are introduced.

Where Pith is reading between the lines

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

  • The framework could be used to compare the knowledge requirements of different randomized consensus algorithms that tolerate different numbers of rounds.
  • Extending the logic to unbounded rounds would allow epistemic analysis of algorithms that continue until they succeed with high probability.
  • The correspondence between information level and epistemic formulas suggests that other operational notions in distributed computing may admit direct translations into knowledge operators.

Load-bearing premise

The framework's definitions of probabilistic knowledge and indistinguishability correctly capture the behavior of randomized algorithms under adversarial message loss in bounded-round executions.

What would settle it

An explicit execution trace of the Varghese-Lynch algorithm in which two processes reach different decisions after the claimed number of rounds while satisfying the paper's epistemic conditions would falsify the strengthened lower bound.

read the original abstract

The coordinated attack problem models the challenge of coordinating a joint action within a bounded time by communicating over unreliable links. It was the first distributed computing problem proven unsolvable. Its analysis also revealed the importance of common knowledge, a central concept in epistemic logic. However, the randomized version of coordinated attack, which is solvable, has not, to the best of our knowledge, been studied through the lens of probabilistic epistemic logic, where processes generate randomness by flipping coins. We present an epistemic logic framework for studying randomized algorithms that execute for a bounded number of rounds. The framework applies to coordinated attack, approximate agreement, and consensus, and supports dynamic graph models: synchronous systems in which reliable processes execute a bounded number of rounds while an adversary determines which messages are lost. Our approach combines techniques from the logical characterization of dynamic networks and task solvability with ideas from probabilistic dynamic epistemic logic. It is inspired by the operational model of Varghese and Lynch for randomized coordinated attack. More broadly, the resulting notion of probabilistic epistemic task solvability provides a foundation for the epistemic study of randomized distributed computation. Using this framework, we analyze the Varghese-Lynch algorithm from a knowledge-theoretic perspective, providing a formal treatment of the algorithm and its lower bound. As a byproduct, we strengthen the lower bound and show it is tight. The proof relies on indistinguishability arguments, demonstrating that reasoning about knowledge remains essential in the probabilistic setting. We also formalize the notion of information level introduced by Varghese and Lynch, showing that it corresponds to a specific epistemic formula.

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.

Referee Report

0 major / 2 minor

Summary. The paper introduces an epistemic logic framework for bounded-round randomized algorithms executing in dynamic graph models (synchronous systems with an adversary controlling message loss). It combines techniques from the logical characterization of dynamic networks and task solvability with probabilistic dynamic epistemic logic, inspired by the Varghese-Lynch operational model. The framework is applied to the randomized coordinated attack problem: the Varghese-Lynch algorithm receives a formal knowledge-theoretic treatment, its lower bound is strengthened, and the bound is shown to be tight via indistinguishability arguments. As a byproduct, the information level from Varghese-Lynch is formalized as a specific epistemic formula. The work positions the resulting notion of probabilistic epistemic task solvability as a foundation for the epistemic study of randomized distributed computation, with applicability noted to approximate agreement and consensus.

Significance. If the framework correctly models probabilistic knowledge and indistinguishability in the presence of coin flips and adversarial message loss, the contribution is significant: it extends epistemic logic to randomized distributed algorithms, demonstrates that knowledge-based reasoning remains essential even in the probabilistic setting, and delivers a strengthened, tight lower bound for randomized coordinated attack. The formalization of information level as an epistemic formula and the explicit use of indistinguishability arguments are concrete strengths. The paper provides a reusable framework rather than ad-hoc analysis, which supports further work on epistemic characterizations of randomized task solvability.

minor comments (2)
  1. The abstract and introduction would benefit from an explicit statement of the precise probabilistic epistemic task solvability definition (likely in §3 or §4) early on, to make the central modeling choice immediately visible to readers familiar with Varghese-Lynch.
  2. Notation for the probabilistic knowledge operators and the dynamic graph model could be clarified with a small table comparing them to the corresponding non-probabilistic operators from prior epistemic logic work on dynamic networks.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the detailed and positive assessment of our manuscript, including the recognition of the framework's novelty in combining epistemic logic with probabilistic elements for randomized distributed algorithms, the strengthened lower bound for randomized coordinated attack, and the formalization of information level. The recommendation for minor revision is noted; we will address any editorial or minor clarifications in the revised version.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces a novel epistemic logic framework for bounded-round randomized algorithms in dynamic graphs, combining logical characterizations of dynamic networks with probabilistic dynamic epistemic logic. It applies this framework to the independently developed Varghese-Lynch algorithm (external prior work), formalizes their information level concept as an epistemic formula, and strengthens the lower bound via indistinguishability arguments. No load-bearing steps reduce by construction to inputs, no self-citations of the authors' own prior results are used to justify uniqueness or central premises, and no fitted parameters are relabeled as predictions. The derivation chain relies on standard epistemic techniques applied to the probabilistic setting and remains independent of the modeled inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on combining existing techniques from logical characterization of dynamic networks and probabilistic dynamic epistemic logic, plus the operational model of Varghese and Lynch; no free parameters or invented entities are mentioned.

axioms (2)
  • domain assumption The operational model of Varghese and Lynch accurately models randomized coordinated attack in dynamic networks
    The framework is explicitly inspired by and applies to this model.
  • domain assumption Indistinguishability arguments remain valid in the probabilistic epistemic setting
    The proof of the strengthened lower bound relies on these arguments.

pith-pipeline@v0.9.1-grok · 5815 in / 1321 out tokens · 27936 ms · 2026-06-26T22:48:28.835891+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 37 canonical work pages

  1. [1]

    2019 , url =

    Wait-Free Solvability of Equality Negation Tasks , booktitle =. 2019 , url =. doi:10.4230/LIPICS.DISC.2019.21 , timestamp =

    work page doi:10.4230/lipics.disc.2019.21 2019

  2. [2]

    A dynamic epistemic logic analysis of equality negation and other epistemic covering tasks , journal =

    Hans van Ditmarsch and. A dynamic epistemic logic analysis of equality negation and other epistemic covering tasks , journal =. 2021 , url =. doi:10.1016/J.JLAMP.2021.100662 , timestamp =

    work page doi:10.1016/j.jlamp.2021.100662 2021

  3. [3]

    Agreement is Harder than Consensus: Set Consensus Problems in Totally Asynchronous Systems , booktitle =

    Soma Chaudhuri , editor =. Agreement is Harder than Consensus: Set Consensus Problems in Totally Asynchronous Systems , booktitle =. 1990 , url =. doi:10.1145/93385.93431 , timestamp =

    work page doi:10.1145/93385.93431 1990

  4. [4]

    Distributed Computing: Fundamentals, Simulations and Advanced Topics , year =

    Attiya, Hagit and Welch, Jennifer , date-modified =. Distributed Computing: Fundamentals, Simulations and Advanced Topics , year =

  5. [6]

    2021 , url =

    A simplicial complex model for dynamic epistemic logic to study distributed task computability , journal =. 2021 , url =. doi:10.1016/J.IC.2020.104597 , timestamp =

    work page doi:10.1016/j.ic.2020.104597 2021

  6. [7]

    Halpern , editor =

    Joseph Y. Halpern , editor =. Reasoning About Uncertainty , year =

  7. [8]

    Pattern Models:

    Armando Casta. Pattern Models:. Comput. J. , volume =. 2024 , url =. doi:10.1093/COMJNL/BXAE016 , timestamp =

    work page doi:10.1093/comjnl/bxae016 2024

  8. [9]

    The Time Complexity of Consensus Under Oblivious Message Adversaries , url =

    Winkler, Kyrill and Paz, Ami and Galeana, Hugo Rincon and Schmid, Stefan and Schmid, Ulrich , date =. The Time Complexity of Consensus Under Oblivious Message Adversaries , url =. Algorithmica , number =. 2024 , bdsk-url-1 =. doi:10.1007/s00453-024-01209-4 , id =

    work page doi:10.1007/s00453-024-01209-4 2024

  9. [10]

    Time is Not a Healer , booktitle =

    Nicola Santoro and Peter Widmayer , editor =. Time is Not a Healer , booktitle =. 1989 , url =. doi:10.1007/BFB0028994 , timestamp =

    work page doi:10.1007/bfb0028994 1989

  10. [11]

    2002 , url =

    Yoram Moses and Sergio Rajsbaum , title =. 2002 , url =. doi:10.1137/S0097539799364006 , timestamp =

    work page doi:10.1137/s0097539799364006 2002

  11. [12]

    Tight Bounds for Asymptotic and Approximate Consensus , journal =

    Matthias F. Tight Bounds for Asymptotic and Approximate Consensus , journal =. 2021 , url =. doi:10.1145/3485242 , timestamp =

    work page doi:10.1145/3485242 2021

  12. [13]

    Akkoyunlu, E. A. and Ekanadham, K. and Huber, R. V. , title =. Proceedings of the Fifth ACM Symposium on Operating Systems Principles , pages =. 1975 , isbn =. doi:10.1145/800213.806523 , abstract =

    work page doi:10.1145/800213.806523 1975

  13. [14]

    Operating Systems, An Advanced Course , pages =

    Gray, Jim , title =. Operating Systems, An Advanced Course , pages =. 1978 , isbn =

    1978

  14. [15]

    Proceedings of the 43rd ACM Symposium on Principles of Distributed Computing , pages =

    Civit, Pierre and Gilbert, Seth and Guerraoui, Rachid and Komatovic, Jovan and Paramonov, Anton and Vidigueira, Manuel , title =. Proceedings of the 43rd ACM Symposium on Principles of Distributed Computing , pages =. 2024 , isbn =. doi:10.1145/3662158.3662780 , abstract =

    work page doi:10.1145/3662158.3662780 2024

  15. [16]

    On the Validity of Consensus , booktitle =

    Pierre Civit and Seth Gilbert and Rachid Guerraoui and Jovan Komatovic and Manuel Vidigueira , editor =. On the Validity of Consensus , booktitle =. 2023 , url =. doi:10.1145/3583668.3594567 , timestamp =

    work page doi:10.1145/3583668.3594567 2023

  16. [17]

    Randomization can be a healer: consensus with dynamic omission failures , url =

    Moniz, Henrique and Neves, Nuno Ferreira and Correia, Miguel and Ver. Randomization can be a healer: consensus with dynamic omission failures , url =. Distributed Computing , number =. 2011 , bdsk-url-1 =. doi:10.1007/s00446-010-0116-2 , id =

    work page doi:10.1007/s00446-010-0116-2 2011

  17. [18]

    How to safely close a discussion , url =

    Gildas Avoine and Serge Vaudenay , doi =. How to safely close a discussion , url =. Information Processing Letters , keywords =. 2007 , bdsk-url-1 =

    2007

  18. [19]

    A logic of blockchain updates , journal =

    Kai Br. A logic of blockchain updates , journal =. 2020 , url =. doi:10.1093/LOGCOM/EXAA045 , timestamp =

    work page doi:10.1093/logcom/exaa045 2020

  19. [20]

    Halpern and Rafael Pass , editor =

    Joseph Y. Halpern and Rafael Pass , editor =. A Knowledge-Based Analysis of the Blockchain Protocol , booktitle =. 2017 , url =. doi:10.4204/EPTCS.251.22 , timestamp =

    work page doi:10.4204/eptcs.251.22 2017

  20. [21]

    Werner, D

    Guy Goren and Yoram Moses and Alexander Spiegelman , editor =. Probabilistic Indistinguishability and the Quality of Validity in Byzantine Agreement , booktitle =. 2022 , url =. doi:10.1145/3558535.3559789 , timestamp =

    work page doi:10.1145/3558535.3559789 2022

  21. [22]

    Probable Approximate Coordination , booktitle =

    Ariel Livshits and Yoram Moses , editor =. Probable Approximate Coordination , booktitle =. 2023 , url =. doi:10.4230/LIPICS.OPODIS.2023.19 , timestamp =

    work page doi:10.4230/lipics.opodis.2023.19 2023

  22. [23]

    Lynch , title =

    George Varghese and Nancy A. Lynch , title =. Inf. Comput. , volume =. 1996 , url =. doi:10.1006/INCO.1996.0063 , timestamp =

    work page doi:10.1006/inco.1996.0063 1996

  23. [24]

    Lynch , title =

    Nancy A. Lynch , title =. 1996 , isbn =

    1996

  24. [25]

    2025 , eprint=

    Notes on Theory of Distributed Systems , author=. 2025 , eprint=

    2025

  25. [26]

    , date =

    Kooi, Barteld P. , date =. Probabilistic Dynamic Epistemic Logic , url =. Journal of Logic, Language and Information , number =. 2003 , bdsk-url-1 =. doi:10.1023/A:1025050800836 , id =

    work page doi:10.1023/a:1025050800836 2003

  26. [27]

    Bisimulations on Planet Kripke , author =

  27. [29]

    Logic and Probabilistic Update

    Demey, Lorenz and Kooi, Barteld. Logic and Probabilistic Update. Johan van Benthem on Logic and Information Dynamics. 2014. doi:10.1007/978-3-319-06025-5_13

    work page doi:10.1007/978-3-319-06025-5_13 2014

  28. [30]

    A Symbolic Representation for Probabilistic Dynamic Epistemic Logic , year =

    Gamblin, S\'. A Symbolic Representation for Probabilistic Dynamic Epistemic Logic , year =. Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems , pages =

  29. [31]

    A dynamic epistemic framework for reasoning about conformant probabilistic plans , journal =

    Yanjun Li and Barteld Kooi and Yanjing Wang , keywords =. A dynamic epistemic framework for reasoning about conformant probabilistic plans , journal =. 2019 , issn =. doi:https://doi.org/10.1016/j.artint.2018.12.001 , url =

    work page doi:10.1016/j.artint.2018.12.001 2019

  30. [32]

    Dynamic Update with Probabilities , url =

    van Benthem, Johan and Gerbrandy, Jelle and Kooi, Barteld , date =. Dynamic Update with Probabilities , url =. Studia Logica , number =. 2009 , bdsk-url-1 =. doi:10.1007/s11225-009-9209-y , id =

    work page doi:10.1007/s11225-009-9209-y 2009

  31. [33]

    Hanabi (card game) --- W ikipedia , The Free Encyclopedia

    Wikipedia. Hanabi (card game) --- W ikipedia , The Free Encyclopedia. 2025

    2025

  32. [34]

    Epistemic Probability Logic Simplified , booktitle =

    Jan van Eijck and Fran. Epistemic Probability Logic Simplified , booktitle =. 2014 , url =

    2014

  33. [35]

    Logics of communication and change , journal =

    Johan van Benthem and Jan van Eijck and Barteld Kooi , keywords =. Logics of communication and change , journal =. 2006 , issn =. doi:https://doi.org/10.1016/j.ic.2006.04.006 , url =

    work page doi:10.1016/j.ic.2006.04.006 2006

  34. [36]

    and Tuttle, Mark R

    Halpern, Joseph Y. and Tuttle, Mark R. , title =. J. ACM , month = sep, pages =. 1993 , issue_date =. doi:10.1145/153724.153770 , abstract =

    work page doi:10.1145/153724.153770 1993

  35. [37]

    Conditional Probability Meets Update Logic , url =

    van Benthem, Johan , date =. Conditional Probability Meets Update Logic , url =. Journal of Logic, Language and Information , number =. 2003 , bdsk-url-1 =. doi:10.1023/A:1025002917675 , id =

    work page doi:10.1023/a:1025002917675 2003

  36. [38]

    Logic Journal of the IGPL , volume =

    Ognjanović, Zoran and Ilić Stepić, Angelina and Perović, Aleksandar , title =. Logic Journal of the IGPL , volume =. 2022 , month =. doi:10.1093/jigpal/jzac072 , url =

    work page doi:10.1093/jigpal/jzac072 2022

  37. [39]

    The structure of epistemic probabilities , url =

    Climenhaga, Nevin , date =. The structure of epistemic probabilities , url =. Philosophical Studies , number =. 2020 , bdsk-url-1 =. doi:10.1007/s11098-019-01367-0 , id =

    work page doi:10.1007/s11098-019-01367-0 2020

  38. [40]

    Halpern and Yoram Moses and Moshe Y

    Ronald Fagin and Joseph Y. Halpern and Yoram Moses and Moshe Y. Vardi , title =. 1995 , url =. doi:10.7551/MITPRESS/5803.001.0001 , isbn =

    work page doi:10.7551/mitpress/5803.001.0001 1995

  39. [41]

    Leslie Lamport , title =. Commun. 1978 , url =. doi:10.1145/359545.359563 , timestamp =

    work page doi:10.1145/359545.359563 1978

  40. [42]

    Knowledge and Belief: An Introduction to the Logic of the Two Notions , year =

    Kaarlo Jaakko Juhani Hintikka , editor =. Knowledge and Belief: An Introduction to the Logic of the Two Notions , year =

  41. [43]

    The asynchronous computability theorem for t-resilient tasks , booktitle =

    Maurice Herlihy and Nir Shavit , editor =. The asynchronous computability theorem for t-resilient tasks , booktitle =. 1993 , url =. doi:10.1145/167088.167125 , timestamp =

    work page doi:10.1145/167088.167125 1993

  42. [44]

    Schneider

    Bowen Alpern and Fred B. Schneider , title =. Inf. Process. Lett. , volume =. 1985 , url =. doi:10.1016/0020-0190(85)90056-0 , timestamp =

    work page doi:10.1016/0020-0190(85)90056-0 1985

  43. [45]

    Halpern and Moshe Y

    Ronald Fagin and Joseph Y. Halpern and Moshe Y. Vardi , title =. J. 1992 , url =. doi:10.1145/128749.150945 , timestamp =

    work page doi:10.1145/128749.150945 1992

  44. [46]

    Dynamic Epistemic Logic , year =

    Hans van Ditmarsch and Wiebe van der Hoek and Barteld Kooi , editor =. Dynamic Epistemic Logic , year =

  45. [47]

    Coordination Through Stochastic Channels , booktitle =

    Pierre Fraigniaud and Boaz Patt. Coordination Through Stochastic Channels , booktitle =. 2025 , url =. doi:10.4230/LIPICS.DISC.2025.32 , timestamp =

    work page doi:10.4230/lipics.disc.2025.32 2025

  46. [48]

    A topological perspective on distributed network algorithms , journal =

    Armando Casta. A topological perspective on distributed network algorithms , journal =. 2021 , url =. doi:10.1016/J.TCS.2020.10.012 , timestamp =

    work page doi:10.1016/j.tcs.2020.10.012 2021

  47. [49]

    39th International Symposium on Theoretical Aspects of Computer Science,

    A Simplicial Model for KB4. 39th International Symposium on Theoretical Aspects of Computer Science,. 2022 , url =. doi:10.4230/LIPICS.STACS.2022.33 , timestamp =

    work page doi:10.4230/lipics.stacs.2022.33 2022

  48. [50]

    Knowledge and simplicial complexes , journal =

    Hans van Ditmarsch and Eric Goubault and J. Knowledge and simplicial complexes , journal =. 2020 , url =. 2002.08863 , timestamp =

    arXiv 2020

  49. [51]

    Halpern , title =

    Ronald Fagin and Joseph Y. Halpern , title =. J. 1994 , url =. doi:10.1145/174652.174658 , timestamp =

    work page doi:10.1145/174652.174658 1994

  50. [52]

    Fischer and Nancy A

    Michael J. Fischer and Nancy A. Lynch and Mike Paterson , title =. J. 1985 , url =. doi:10.1145/3149.214121 , timestamp =

    work page doi:10.1145/3149.214121 1985