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Documents authored by Mendes, Hammurabi

Document
DOI: 10.4230/LIPIcs.OPODIS.2024.8
Optimal Multilevel Slashing for Blockchains

Authors: Kenan Wood, Hammurabi Mendes, and Jonad Pulaj

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
We present the notion of multilevel slashing, where proof-of-stake blockchain validators can obtain gradual levels of assurance that a certain block is bound to be finalized in a global consensus procedure, unless an increasing and optimally large number of Byzantine processes have their staked assets slashed - that is, deducted - due to provably incorrect behavior. Our construction is a highly parameterized generalization of combinatorial intersection systems based on finite projective spaces, with asymptotic high availability and optimal slashing properties. Even under weak conditions, we show that our construction has asymptotically optimal slashing properties with respect to message complexity and validator load; this result also illustrates a fundamental trade off between message complexity, load, and slashing. In addition, we show that any intersection system whose ground elements are disjoint subsets of nodes (e.g. "committees" in committee-based consensus protocols) has asymptotic high availability under similarly weak conditions. Finally, our multilevel construction gives the flexibility to blockchain validators to decide how many "levels" of finalization assurance they wish to obtain. This functionality can be seen either as (i) a form of an early, slashing-based block finalization; or (ii) a service to support reorg tolerance.
Cite as

Kenan Wood, Hammurabi Mendes, and Jonad Pulaj. Optimal Multilevel Slashing for Blockchains. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wood_et_al:LIPIcs.OPODIS.2024.8,
  author =	{Wood, Kenan and Mendes, Hammurabi and Pulaj, Jonad},
  title =	{{Optimal Multilevel Slashing for Blockchains}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.8},
  URN =		{urn:nbn:de:0030-drops-225445},
  doi =		{10.4230/LIPIcs.OPODIS.2024.8},
  annote =	{Keywords: Blockchains, Finality, Slashablility, Committees, Availability}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.32
Distributed Agreement in the Arrovian Framework

Authors: Kenan Wood, Hammurabi Mendes, and Jonad Pulaj

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
Preference aggregation is a fundamental problem in voting theory, in which public input rankings of a set of alternatives (called preferences) must be aggregated into a single preference that satisfies certain soundness properties. The celebrated Arrow Impossibility Theorem is equivalent to a distributed task in a synchronous fault-free system that satisfies properties such as respecting unanimous preferences, maintaining independence of irrelevant alternatives (IIA), and non-dictatorship, along with consensus since only one preference can be decided. In this work, we study a weaker distributed task in which crash faults are introduced, IIA is not required, and the consensus property is relaxed to either k-set agreement or ε-approximate agreement using any metric on the set of preferences. In particular, we prove several novel impossibility results for both of these tasks in both synchronous and asynchronous distributed systems. We additionally show that the impossibility for our ε-approximate agreement task using the Kendall tau or Spearman footrule metrics holds under extremely weak assumptions.
Cite as

Kenan Wood, Hammurabi Mendes, and Jonad Pulaj. Distributed Agreement in the Arrovian Framework. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wood_et_al:LIPIcs.OPODIS.2024.32,
  author =	{Wood, Kenan and Mendes, Hammurabi and Pulaj, Jonad},
  title =	{{Distributed Agreement in the Arrovian Framework}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.32},
  URN =		{urn:nbn:de:0030-drops-225686},
  doi =		{10.4230/LIPIcs.OPODIS.2024.32},
  annote =	{Keywords: Approximate Agreement, Set Agreement, Preference Aggregation, Voting Theory, Impossibility}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.35
Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems

Authors: Hammurabi Mendes and Maurice Herlihy

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
In this paper, we show that the protocol complex of a Byzantine synchronous system can remain (k-1)-connected for up to ceil(t/k) rounds, where t is the maximum number of Byzantine processes, and t >= k >= 1. This topological property implies that ceil(t/k) + 1 rounds are necessary to solve k-set agreement in Byzantine synchronous systems, compared to floor(t/k) + 1 rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine k-set agreement in exactly ceil(t/k) + 1 synchronous rounds, at least when n is suitably large compared to t. In conclusion, we see how Byzantine failures can potentially require one extra round to solve k-set agreement, and, for n suitably large compared to t, at most that.
Cite as

Hammurabi Mendes and Maurice Herlihy. Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mendes_et_al:LIPIcs.DISC.2017.35,
  author =	{Mendes, Hammurabi and Herlihy, Maurice},
  title =	{{Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.35},
  URN =		{urn:nbn:de:0030-drops-79930},
  doi =		{10.4230/LIPIcs.DISC.2017.35},
  annote =	{Keywords: Byzantine, synchronous, k-set agreement, topology, connectivity}
}
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