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Documents authored by Gafni, Eli

Document
DOI: 10.4230/LIPIcs.OPODIS.2025.21
Solving Tasks with Fewer Registers Than Processes

Authors: Eli Gafni, Giuliano Losa, Michel Raynal, and Gadi Taubenfeld

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
This paper studies distributed-computing tasks through the lens of space complexity in the read/write wait-free model, defined as the number of multi-reader-multi-writer atomic read/write registers needed to solve a task using a wait-free algorithm. Surprisingly, even though the read/write wait-free model is at the foundation of distributed computing, previous work on space complexity has focused on synchronization primitives stronger than read/write registers or on weaker progress conditions. The paper reveals that the read/write wait-free model offers a rich space-complexity landscape: (1) assuming non-anonymous processes, it shows that there is an infinite hierarchy of tasks of increasing space complexity; (2) it shows that space complexity separates anonymous from non-anonymous memory; (3) regardless of process or register anonymity, it exhibits a task of space complexity two, which is the minimal non-trivial space complexity; (4) finally, it shows that subcases of the adopt-commit task have different space complexity in non-anonymous memory under bounded wait-freedom.
Cite as

Eli Gafni, Giuliano Losa, Michel Raynal, and Gadi Taubenfeld. Solving Tasks with Fewer Registers Than Processes. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gafni_et_al:LIPIcs.OPODIS.2025.21,
  author =	{Gafni, Eli and Losa, Giuliano and Raynal, Michel and Taubenfeld, Gadi},
  title =	{{Solving Tasks with Fewer Registers Than Processes}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{21:1--21:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.21},
  URN =		{urn:nbn:de:0030-drops-251947},
  doi =		{10.4230/LIPIcs.OPODIS.2025.21},
  annote =	{Keywords: Asynchrony, Read/write registers, Wait-freedom, Tasks, Covering argument, Lower bound, Space complexity, Anonymous Processes, Anonymous Memory}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.29
How Exhaustive Does an Extension-Based Proof Need to Be?

Authors: Faith Ellen, Shihao Liu, Leqi Zhu, Eli Gafni, and Rati Gelashvili

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The class of extension-based proofs encompasses traditional valency arguments. It has been shown that they are insufficient to establish the impossibility of (n-1)-set agreement among n ≥ 3 processes in an asynchronous system with crash failures. We generalize this definition to k-exhaustive extension-based proofs, in which a prover can learn the maximum length of all executions involving a set of at most k processes from a specified configuration (which may be infinite). An upper bound on the length of these executions enables the prover to determine the outputs of all these executions. When k = n, this enables the prover to perform an exhaustive search of all reachable configurations, so it knows everything about the protocol. On the other hand, extension based proofs are as powerful as 1-exhaustive extension-based proofs. For any task with no deterministic, wait-free solution among n ≥ 2 processes, we show that there is an (n-1)-exhaustive extension-based proof of its impossibility. This is done using a new characterization of such tasks. In contrast, we prove that for 1 ≤ k ≤ n-2, there is no k-exhaustive extension-based proof of the impossibility of (n-1)-set agreement.
Cite as

Faith Ellen, Shihao Liu, Leqi Zhu, Eli Gafni, and Rati Gelashvili. How Exhaustive Does an Extension-Based Proof Need to Be?. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ellen_et_al:LIPIcs.OPODIS.2025.29,
  author =	{Ellen, Faith and Liu, Shihao and Zhu, Leqi and Gafni, Eli and Gelashvili, Rati},
  title =	{{How Exhaustive Does an Extension-Based Proof Need to Be?}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.29},
  URN =		{urn:nbn:de:0030-drops-252020},
  doi =		{10.4230/LIPIcs.OPODIS.2025.29},
  annote =	{Keywords: Extension-based proof, set agreement, valency argument, zero-one exclusion}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2023.41
Brief Announcement: Byzantine Consensus Under Dynamic Participation with a Well-Behaved Majority

Authors: Eli Gafni and Giuliano Losa

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
In a permissionless system like Ethereum, participation may fluctuate dynamically as some participants unpredictably go offline and some others come back online. In such an environment, traditional Byzantine fault-tolerant consensus algorithms may stall - even in the absence of failures - because they rely on the availability of fixed-sized quorums. The sleepy model formally captures the main requirements for solving consensus under dynamic participation, and several algorithms solve consensus with probabilistic safety in this model assuming that, at any time, more than half of the online participants are well behaved. However, whether safety can be ensured deterministically under these assumptions, especially with constant latency, remained an open question. Assuming a constant adversary, we answer in the positive by presenting a consensus algorithm that achieves deterministic safety and constant latency in expectation. In the full version of this paper, we also present a second algorithm which obtains both deterministic safety and liveness, but is likely only of theoretical interest because of its high round and message complexity. Both algorithms are striking in their simplicity.
Cite as

Eli Gafni and Giuliano Losa. Brief Announcement: Byzantine Consensus Under Dynamic Participation with a Well-Behaved Majority. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 41:1-41:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gafni_et_al:LIPIcs.DISC.2023.41,
  author =	{Gafni, Eli and Losa, Giuliano},
  title =	{{Brief Announcement: Byzantine Consensus Under Dynamic Participation with a Well-Behaved Majority}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{41:1--41:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.41},
  URN =		{urn:nbn:de:0030-drops-191675},
  doi =		{10.4230/LIPIcs.DISC.2023.41},
  annote =	{Keywords: Consensus, Sleepy Model, Dynamic Participation, Byzantine Failures}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.27
Stellar Consensus by Instantiation

Authors: Giuliano Losa, Eli Gafni, and David Mazières

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
Stellar introduced a new type of quorum system called a Federated Byzantine Agreement System. A major difference between this novel type of quorum system and a threshold quorum system is that each participant has its own, personal notion of a quorum. Thus, unlike in a traditional BFT system, designed for a uniform notion of quorum, even in a time of synchrony one well-behaved participant may observe a quorum of well-behaved participants, while others may not. To tackle this new problem in a more general setting, we abstract the Stellar Network as an instance of what we call Personal Byzantine Quorum Systems. Using this notion, we streamline the theory behind the Stellar Network, removing the clutter of unnecessary details, and refute the conjecture that Stellar’s notion of intact set is optimally fault-tolerant. Most importantly, we develop a new consensus algorithm for the new setting.
Cite as

Giuliano Losa, Eli Gafni, and David Mazières. Stellar Consensus by Instantiation. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{losa_et_al:LIPIcs.DISC.2019.27,
  author =	{Losa, Giuliano and Gafni, Eli and Mazi\`{e}res, David},
  title =	{{Stellar Consensus by Instantiation}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.27},
  URN =		{urn:nbn:de:0030-drops-113343},
  doi =		{10.4230/LIPIcs.DISC.2019.27},
  annote =	{Keywords: Consensus, Stellar, Partial Synchrony, Byzantine Fault Tolerance}
}
Document
DOI: 10.4230/LIPIcs.DISC.2018.17
A Wealth of Sub-Consensus Deterministic Objects

Authors: Eli Daian, Giuliano Losa, Yehuda Afek, and Eli Gafni

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract
The consensus hierarchy classifies shared an object according to its consensus number, which is the maximum number of processes that can solve consensus wait-free using the object. The question of whether this hierarchy is precise enough to fully characterize the synchronization power of deterministic shared objects was open until 2016, when Afek et al. showed that there is an infinite hierarchy of deterministic objects, each weaker than the next, which is strictly between i and i+1-processors consensus, for i >= 2. For i=1, the question whether there exist a deterministic object whose power is strictly between read-write and 2-processors consensus, remained open. We resolve the question positively by exhibiting an infinite hierarchy of simple deterministic objects which are equivalent to set-consensus tasks, and thus are stronger than read-write registers, but they cannot implement consensus for two processes. Still our paper leaves a gap with open questions.
Cite as

Eli Daian, Giuliano Losa, Yehuda Afek, and Eli Gafni. A Wealth of Sub-Consensus Deterministic Objects. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{daian_et_al:LIPIcs.DISC.2018.17,
  author =	{Daian, Eli and Losa, Giuliano and Afek, Yehuda and Gafni, Eli},
  title =	{{A Wealth of Sub-Consensus Deterministic Objects}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.17},
  URN =		{urn:nbn:de:0030-drops-98061},
  doi =		{10.4230/LIPIcs.DISC.2018.17},
  annote =	{Keywords: shared memory, distributed algorithms, wait-free, set consensus}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2016.6
Read-Write Memory and k-Set Consensus as an Affine Task

Authors: Eli Gafni, Yuan He, Petr Kuznetsov, and Thibault Rieutord

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract
The wait-free read-write memory model has been characterized as an iterated Immediate Snapshot (IS) task. The IS task is affine — it can be defined as a (sub)set of simplices of the standard chromatic subdivision. In this paper, we highlight the phenomenon of a "natural" model that can be captured by an iterated affine task and, thus, by a subset of runs of the iterated immediate snapshot model. We show that the read-write memory model in which, additionally, k-set-consensus objects can be used is "natural" by presenting the corresponding simple affine task captured by a subset of 2-round IS runs. As an "unnatural" example, the model using the abstraction of Weak Symmetry Breaking (WSB) cannot be captured by a set of IS runs and, thus, cannot be represented as an affine task. Our results imply the first combinatorial characterization of models equipped with abstractions other than read-write memory that applies to generic tasks.
Cite as

Eli Gafni, Yuan He, Petr Kuznetsov, and Thibault Rieutord. Read-Write Memory and k-Set Consensus as an Affine Task. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gafni_et_al:LIPIcs.OPODIS.2016.6,
  author =	{Gafni, Eli and He, Yuan and Kuznetsov, Petr and Rieutord, Thibault},
  title =	{{Read-Write Memory and k-Set Consensus as an Affine Task}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.6},
  URN =		{urn:nbn:de:0030-drops-70759},
  doi =		{10.4230/LIPIcs.OPODIS.2016.6},
  annote =	{Keywords: iterated affine tasks, k-set consensus, k-concurrency, simplicial complexes, immediate snapshot}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2016.7
Set-Consensus Collections are Decidable

Authors: Carole Delporte-Gallet, Hugues Fauconnier, Eli Gafni, and Petr Kuznetsov

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)

Abstract
A natural way to measure the power of a distributed-computing model is to characterize the set of tasks that can be solved in it. In general, however, the question of whether a given task can be solved in a given model is undecidable, even if we only consider the wait-free shared-memory model. In this paper, we address this question for restricted classes of models and tasks. We show that the question of whether a collection C of (l, j)-set consensus objects, for various l (the number of processes that can invoke the object) and j (the number of distinct outputs the object returns), can be used by n processes to solve wait-free k-set consensus is decidable. Moreover, we provide a simple O(n^2) decision algorithm, based on a dynamic programming solution to the Knapsack optimization problem. We then present an adaptive wait-free set-consensus algorithm that, for each set of participating processes, achieves the best level of agreement that is possible to achieve using C. Overall, this gives us a complete characterization of a read-write model defined by a collection of set-consensus objects through its set-consensus power.
Cite as

Carole Delporte-Gallet, Hugues Fauconnier, Eli Gafni, and Petr Kuznetsov. Set-Consensus Collections are Decidable. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{delportegallet_et_al:LIPIcs.OPODIS.2016.7,
  author =	{Delporte-Gallet, Carole and Fauconnier, Hugues and Gafni, Eli and Kuznetsov, Petr},
  title =	{{Set-Consensus Collections are Decidable}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.7},
  URN =		{urn:nbn:de:0030-drops-70761},
  doi =		{10.4230/LIPIcs.OPODIS.2016.7},
  annote =	{Keywords: Decidability, distributed tasks, set consensus, Knapsack problem}
}
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