Over the past years, distributed consensus research has shifted its focus towards addressing challenges in large-scale, permissionless systems, such as blockchains. This shift is characterized by the need to accommodate dynamic participation, contrasting the traditional approach of a static set of continuously online participants. Works like Bitcoin and the Sleepy Model have set the stage for this developing framework. Notable contributions from Momose and Ren (CCS 2022) and subsequent works have introduced Total-Order Broadcast protocols leveraging Graded Agreement primitives and supporting dynamic participation, though often requiring multiple rounds of voting per decision -- a potential bottleneck for real-world large-scale systems. Addressing this, our paper presents a novel Total-Order Broadcast protocol in the Sleepy Model resilient to up to 1/2 adversarial participants, requiring just a single round of voting per decision. This work paves the way to more practical Total-Order Broadcast protocols to be implemented in real-world systems where a large number of participants are involved simultaneously and their participation level might fluctuate over time.
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