In Byzantine agreement with predictions each process begins with an input value and some (unreliable) prediction bits. Recently, it has been shown that with classification predictions—where the predictions predict each process to be honest or faulty—Byzantine agreement can be completed more quickly than without predictions, circumventing the traditional Ω(f) round lower bound. However, existing algorithms either handle limited prediction errors or send too many messages. Moreover, they all exchange Ω(n3) bits—enough to allow the processes to approximately agree on the classifications. In fact, it almost seemed necessary to share a significant number of prediction bits if one wanted to tolerate a high number of incorrect predictions.

We study the problem of Byzantine Agreement with predictions in synchronous message passing systems. Along with a proposal, each process is also given a prediction, i.e., extra information that is not guaranteed to be true. For example, one might imagine that the prediction is produced by a network security monitoring service that looks for patterns of malicious behavior.

Byzantine Agreement (BA) allows n processes to propose input values to reach consensus on a common, valid Lo-bit value, even in the presence of up to t < n faulty processes that can deviate arbitrarily from the protocol. Although strategies like randomization, adaptiveness, and batching have been extensively explored to mitigate the inherent limitations of one-shot agreement tasks, there has been limited progress on achieving good amortized performance for multi-shot agreement, despite its obvious relevance to long-lived functionalities such as state machine replication.

Byzantine agreement allows n processes to decide on a common value, in spite of arbitrary failures. The seminal Dolev-Reischuk bound states that any deterministic solution to Byzantine agreement exchanges Ω(n2) bits. In synchronous networks, with a known upper bound on message delays, solutions with optimal O (n2) bit complexity, optimal fault tolerance, and no cryptography have been established for over three decades. However, these solutions lack robustness under adverse network conditions. Therefore, research has increasingly focused on Byzantine agreement for partially synchronous networks, which behave synchronously only eventually and are thus more reflective of real-world conditions. Numerous solutions have been proposed for the partially synchronous setting. However, these solutions are notoriously hard to prove correct, and the most efficient cryptography-free algorithms still require O (n3) exchanged bits in the worst case. Even with cryptography, the state-of-the-art remains a κ-bit factor away from the Ω(n2) lower bound (where κ is the security parameter). This discrepancy between synchronous and partially synchronous solutions has remained unresolved for decades.

Byzantine Agreement (BA) enables n processes to reach consensus on a common valid Lo-bit value, even in the presence of up to t < n faulty processes that can deviate arbitrarily from their prescribed protocol. Despite its significance, the optimal communication complexity for key variations of BA has not been determined within the honest majority regime (n = 2t +1), for both the worst-case scenario and the adaptive scenario, which accounts for the actual number f ≤ t of failures. We introduce ada-Dare (Adaptively Disperse, Agree, Retrieve), a novel universal approach to solve BA efficiently. Let κ represent the size of the cryptographic objects required to solve BA when t > n/3. Different instantiations of ada-Dare achieve near-optimal adaptive bit complexity of O(nLo + n(f + 1)κ) for both strong multi-valued validated BA (SMVBA) and interactive consistency (IC). By definition, for IC, Lo = nLin where Lin is the size of an input value. These results achieve optimal O(n(Lo + f)) word complexity and significantly improve the previous best results by up to a linear factor, depending on Lo and f.

Abstract The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most $$f < n / 3$$ f < n / 3 failures, any solution to Byzantine consensus exchanges $$\Omega \big (n^2\big )$$ Ω ( n 2 ) words, where a word contains a constant number of values and signatures. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony where the network alternates between (1) asynchronous periods, with unbounded message delays, and (2) synchronous periods, with $$\delta $$ δ -bounded message delays. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing SQuad , a partially synchronous Byzantine consensus protocol with $$O\big (n^2\big )$$ O ( n 2 ) worst-case communication complexity. In addition, SQuad is optimally-resilient (tolerating up to $$f < n / 3$$ f < n / 3 failures) and achieves $$O(f \cdot \delta )$$ O ( f · δ ) worst-case latency complexity. The key technical contribution underlying SQuad lies in the way we solve view synchronization , the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present RareSync , a view synchronization protocol with $$O\big (n^2\big )$$ O ( n 2 ) communication complexity and $$O(f \cdot \delta )$$ O ( f · δ ) latency complexity, which we utilize in order to obtain SQuad .

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic communication complexity in the worst case. While it has been shown that the bound is tight in synchronous environments, it is still unknown whether a consensus protocol with quadratic communication complexity can be obtained in partial synchrony. Until now, the most efficient known solutions for Byzantine consensus in partially synchronous settings had cubic communication complexity (e.g., HotStuff, binary DBFT). This paper closes the existing gap by introducing SQuad, a partially synchronous Byzantine consensus protocol with quadratic worst-case communication complexity. In addition, SQuad is optimally-resilient and achieves linear worst-case latency complexity. The key technical contribution underlying SQuad lies in the way we solve view synchronization, the problem of bringing all correct processes to the same view with a correct leader for sufficiently long. Concretely, we present RareSync, a view synchronization protocol with quadratic communication complexity and linear latency complexity, which we utilize in order to obtain SQuad.

The organizers of the 4th Parameterized Algorithms and Computational Experiments challenge (PACE 2019) report on the 4th iteration of the PACE challenge. This year, the first track featured the MinVertexCover problem, which asks given an undirected graph G=(V,E) to output a set S subseteq V of vertices such that for every edge vw in E at least one endpoint belongs to S. The exact decision version of this problem is one of the most discussed problem if not even the prototypical problem in parameterized complexity theory. Another two tracks were dedicated to computing the hypertree width of a given hypergraph, which is a certain generalization of tree decompositions to hypergraphs that has widely been applied to problems in databases, constraint programming, and artificial intelligence. On one track we asked for submissions that compute hypertree decompositions of minimum width (MinHypertreeWidth) and on the other track we asked to heuristically compute hypertree decompositions of small width quickly (HeurHypertreeWidth). We received 28 implementations from 26 teams. This year we asked participants to submit solver descriptions in order to count as a submission for the challenge. We received those from 16 teams with overall 33 participants from 10 countries. One team submitted successful solutions to all three tracks.