Common use of Message complexity Clause in Contracts

Message complexity. ‌ GWTS executes a possibly infinite sequence of decisions. Thus, we restrict our message complexity analysis to the number of messages needed for each decision. The messages are counted per proposer, we include messages created by correct acceptors in response to proposer actions. Each proposer decides exactly once for each algorithm round. Therefore, we count messages from start to end of a generic round. A proposer has to reliably broadcast its batch (line 15 -cost O(n2)), it has to broadcast its proposal (line 25 - cost O(n)), then, in the worst case, it refines its proposal at most f times (see Lemma 10 -line 33 - cost O(n)), however each ack from a correct acceptor has to be reliably broadcast (line 10 - cost O(n2)). The total cost is therefore upper-bounded by O(f · n2).

Message complexity. ‌ GWTS executes a possibly infinite sequence of decisions. Thus, we restrict our message complexity analysis to the number of messages needed for each decision. The messages are counted per proposer, we include messages created by correct cor- rect acceptors in response to proposer actions. Each proposer decides exactly once for each algorithm round. Therefore, we count messages from start to end of a generic round. A proposer has to reliably broadcast its batch (line 15 -cost O(n2O O (n2)), it has to broadcast its proposal (line 25 - cost O(n(n)), then, in the worst case, it refines its proposal at most f times O (see Lemma 10 -line 33 - cost O(n(n)), however each ack from a correct acceptor has to be reliably broadcast (line 10 - cost O(n2)). The total cost is therefore upper-bounded by O(f · n2O(f·n2).