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Optimality of Simultaneous Consensus with Limited Information Exchange (Extended Abstract)

Kaya Alpturer, Ron van der Meyden, Sushmita Ruj, Godfrey Wong

TL;DR

This work studies simultaneous Byzantine (SBA) agreement under crash failures with limited information exchange. By formalizing information-exchange protocols and a knowledge-based program P^opt, the authors establish SBA-optimal implementations across FloodSet, Counting FloodSet, Vectorized FloodSet, and a novel SendWaste exchange, achieving earliest possible decisions given each exchange. Key results include refined stopping times (e.g., Flood+), optimality proofs for counting variants, and a near-full-information benchmark via SendWaste that reduces communication and computation costs. The framework integrates epistemic logic with distributed protocols to derive practically efficient SBA implementations under constrained communication, laying groundwork for extensions to omission failures and unique-decision requirements.

Abstract

Work on the development of optimal fault-tolerant Agreement protocols using the logic of knowledge has concentrated on the "full information" approach to information exchange, which is costly with respect to message size. Alpturer, Halpern, and van der Meyden (PODC 2023) introduced the notion of optimality with respect to a limited information exchange, and studied the Eventual Agreement problem in the sending omissions failure model. The present paper studies the Simultaneous Agreement problem for the crash failures model, and a number of limited information exchanges from the literature. In particular, the paper considers information exchanges from a FloodSet protocol (Lynch, Distributed Algorithms 1996), a variant of this in which agents also count the number of failures (Castañeda et al, NETYS 2017), and a variant in which agents associate each agent with a value (Raynal, PRDC 2002). A new information exchange is also introduced that enables decisions to be made at worst one round later than the optimal protocol of Dwork and Moses (I&C 88), but with lower computation cost and space requirements. By determining implementations of a knowledge based program, protocols are derived that are optimal amongst protocols for each of these information exchanges.

Optimality of Simultaneous Consensus with Limited Information Exchange (Extended Abstract)

TL;DR

This work studies simultaneous Byzantine (SBA) agreement under crash failures with limited information exchange. By formalizing information-exchange protocols and a knowledge-based program P^opt, the authors establish SBA-optimal implementations across FloodSet, Counting FloodSet, Vectorized FloodSet, and a novel SendWaste exchange, achieving earliest possible decisions given each exchange. Key results include refined stopping times (e.g., Flood+), optimality proofs for counting variants, and a near-full-information benchmark via SendWaste that reduces communication and computation costs. The framework integrates epistemic logic with distributed protocols to derive practically efficient SBA implementations under constrained communication, laying groundwork for extensions to omission failures and unique-decision requirements.

Abstract

Work on the development of optimal fault-tolerant Agreement protocols using the logic of knowledge has concentrated on the "full information" approach to information exchange, which is costly with respect to message size. Alpturer, Halpern, and van der Meyden (PODC 2023) introduced the notion of optimality with respect to a limited information exchange, and studied the Eventual Agreement problem in the sending omissions failure model. The present paper studies the Simultaneous Agreement problem for the crash failures model, and a number of limited information exchanges from the literature. In particular, the paper considers information exchanges from a FloodSet protocol (Lynch, Distributed Algorithms 1996), a variant of this in which agents also count the number of failures (Castañeda et al, NETYS 2017), and a variant in which agents associate each agent with a value (Raynal, PRDC 2002). A new information exchange is also introduced that enables decisions to be made at worst one round later than the optimal protocol of Dwork and Moses (I&C 88), but with lower computation cost and space requirements. By determining implementations of a knowledge based program, protocols are derived that are optimal amongst protocols for each of these information exchanges.

Paper Structure

This paper contains 8 sections, 10 theorems, 3 equations, 1 table, 7 algorithms.

Table of Contents

  1. Introduction
  2. Framework
  3. Optimality and Knowledge-based Programs
  4. FloodSet
  5. Counting Extensions
  6. Vectorized FloodSet
  7. Sending the Waste
  8. Conclusion

Key Result

lemma 1

MT88 Let $r$ be a run of an SBA protocol generating interpreted system $\mathcal{I}$ and let $i\in \mathcal{N}(r,m)$. If $(\mathcal{I},r,m) \models \mathop{\mathrm{deciding}}\nolimits_i(v)$ for $v \in \{0,1\}$, then $(\mathcal{I},r,m) \models C_{\mathcal{N}} (\exists v)$.

Theorems & Definitions (11)

  • lemma 1
  • lemma 2
  • lemma 3
  • Definition 1: Clean Round
  • lemma 4
  • lemma 5
  • theorem 1
  • theorem 2
  • theorem 3
  • theorem 4
  • ...and 1 more