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It has recently been shown that, contrarily to a common belief, money transfer in the presence of faulty (Byzantine) processes does not require strong agreement such as consensus. This article goes one step further: namely, it first proposes a non-sequential specification of the money-transfer object, and then presents a generic algorithm based on a simple FIFO order between each pair of processes that implements it. The genericity dimension lies in the underlying reliable broadcast abstraction which must be suited to the appropriate failure model. Interestingly, whatever the failure model, the money transfer algorithm only requires adding a single sequence number to its messages as control information. Moreover, as a side effect of the proposed algorithm, it follows that money transfer is a weaker problem than the construction of a safe/regular/atomic read/write register in the asynchronous message-passing crash-prone model.
Many blockchain consensus protocols have been proposed recently to scale the throughput of a blockchain with available bandwidth. However, these protocols are becoming increasingly complex, making it more and more difficult to produce proofs of their
We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required.
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By defining t
Modern science and engineering computing environments often feature storage systems of different types, from parallel file systems in high-performance computing centers to object stores operated by cloud providers. To enable easy, reliable, secure, a
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared norm of the