Consensus mechanisms are a core feature for handling negotiation and agreements. Blockchain technology has seen the introduction of different sorts of consensus mechanism, ranging from tasks of heavy computation to the subtle mathematical proofs of Byzantine agreements. This paper presents the pioneer Delegated Byzantine Fault Tolerance (dBFT) protocol of Neo Blockchain, which was inspired by the Practical Byzantine Fault Tolerance (PBFT). Besides introducing its history, this study describes proofs and didactic examples, as well as novel design and extensions for Neo dBFT with multiple block proposals. Finally, we discuss challenges when dealing with strong Byzantine adversaries, and propose solutions inspired on PBFT for current weak-synchrony problems and increasing system robustness against attacks. Key Contribution: Presents an overview of the history of PBFT-inspired consensus for blockchain, highlighting its current importance on the literature, challenges and assumptions. Contributes to the field of Distributed Consensus, proposing novel extensions for the Neo dBFT (dBFT 2.0+, dBFT 3.0 and dBFT 3.0+), with new insights on innovative consensus mechanisms.

This paper describes a successful combination of genetic algorithm and local search procedure to find good solutions for just-in-time job-shop scheduling problem with earliness and tardiness penalties. For each job is given a specific order of machines in which its operations must be processed, and each operation has a due date, a processing time, and earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. The problem is very hard to solve to optimality even for small instances, but the proposed genetic algorithm found good solutions for some problem instances, even improving its performance when a local search procedure is invoked as an additional phase. The quality of the solutions is evaluated and compared to a set of instances from the literature, with up to 20 jobs and 10 machines. The proposed algorithm improved the solution value for most of the instances.

Mixed-integer mathematical programming has been widely used to model and solve challenging optimization problems. One interesting feature of this technique is the ability to prove the optimality of the achieved solution, for many practical scenarios where a linear programming model can be devised. This paper explores its use to model very strong Byzantine adversaries, in the context of distributed consensus systems. In particular, we apply the proposed technique to find challenging adversarial conditions on a state-of-the-art blockchain consensus: the Neo dBFT. Neo Blockchain has been using the dBFT algorithm since its foundation, but, due to the complexity of the algorithm, it is challenging to devise definitive algebraic proofs that guarantee safety/liveness of the system (and adjust for every change proposed by the community). Core developers have to manually devise and explore possible adversarial attacks scenarios as an exhaustive task. The proposed multi-objective model is intended to assist the search of possible faulty scenario, which includes three objective functions that can be combined as a maximization problem for testing one-block finality or a minimization problem for ensuring liveness. Automated graphics help developers to visually observe attack conditions and to quickly find a solution. This paper proposes an exact adversarial model that explores current limits for practical blockchain consensus applications such as dBFT, with ideas that can also be extended to other decentralized ledger technologies.