Lattice Aggregation in Distributed Verification under Crash and Byzantine Failures

2026-06-11

AI Summary

This work investigates how asynchronous distributed systems can collaboratively reconstruct a complete execution trace from partial and potentially overlapping local observations, despite crash or Byzantine failures. It introduces the c-Lattice Aggregation problem, which requires at least c correct processes to output mutually comparable histories, all bounded by a common global trace. By incorporating a redundancy parameter x, the paper establishes, for the first time, tight solvability thresholds under both failure models: x ≥ t+1 for crash failures and x ≥ 2t+c for Byzantine failures. Matching upper and lower bounds are achieved through algorithms based on SCD-broadcast and indistinguishability arguments. Furthermore, the study establishes an equivalence between fault-tolerant verifiability of this problem and the audibility of global dependency properties—such as consensus and linearizability—yielding the first complete characterization of c-Lattice Aggregation in Byzantine environments.

Abstract

We introduce c-Lattice Aggregation, a fault-tolerant reconstruction problem for distributed verification under crash and Byzantine failures. In our setting, n asynchronous processes supervise a concurrent execution I: each process holds a local sample, and must collaboratively reconstruct I from partial, potentially overlapping observations. A protocol solves c-Lattice Aggregation if at least c correct processes output the complete execution I, while all correct outputs are comparable and bounded by I. This strengthens Lattice Agreement [Attiya, Herlihy and Rachman, 1995] and Byzantine Lattice Agreement [Di Luna et al., 2020; Zheng and Garg, 2020]. We parameterize inputs by a redundancy parameter x -- every element of I appears in at least x initial samples -- and establish tight feasibility thresholds. Under crash failures with at most t faulty processes, Lattice Aggregation is solvable if and only if x >= t + 1. Under Byzantine failures with t < n/3, c-Lattice Aggregation is solvable if and only if x >= 2t + c. All bounds are tight: we present matching algorithms based on SCD-broadcast [Imbs et al., 2018; Khanchandani and Wattenhofer, 2024] and indistinguishability-based lower bounds. Finally, we define globally dependent languages -- those for which no partial view can certify correctness, including consensus, linearizability, k-set agreement, and leader election -- and prove that soundness of any monitoring system is achievable if and only if c-Lattice Aggregation is solved, yielding the first complete characterization of fault-tolerant verification under Byzantine failures.

Problem

• Lattice Aggregation
• Byzantine failures
• Crash failures
• Distributed verification
• Fault tolerance

Innovation

• c-Lattice Aggregation
• Byzantine fault tolerance
• distributed verification
• redundancy threshold
• SCD-broadcast