Generalising SbS Clause Samples

Generalising SbS. Adapting the SbS algorithm to its generalised version, while keeping the message complexity improvement, needs a special attention to substitute the reliable broadcast used to acknowledge in the GWTS (line 10 of Algorithm 4). We would like to replace such broadcast with a single point-to- point message. We do this by forcing an acceptor to sign its, now poin-to-point, ack. Intuitively, a proposer is able to prove others that it received an ack for its proposal. Each correct proposer broadcasts a special decided message before deciding, such message has attached all the acks used to decide. This would allow proposers and acceptors that receive a decided message to know that the sender of such message was allowed to decide by the algorithm rules (recall that acks are now signed). Additional details can be found in the full version.
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