January 15, 2021 - 1 min read
BREAK
\(\frac{f_{c} + 1}{2}\)
\(\mathcal{D}\)
\(\mathcal{O}(n)\)
\(\mathcal{S}\)
\(\mathcal{1/3}\)
\(2f_{c} + 1\)
\(f_{c} + 1\)
\(r + 1\)
\(f_{c}\)
\(2f_{d} + 1\)
\(f_{d} + 1\)
\(f_{d}\)
\(b_{1}\)
\(2f_{t} + 1\)
\(2f + 1\)
\(f_{t} + 1\)
\(f_{t}\)
\(3f_{t} + 1\)
\(\frac{1}{3}\)
\(S_{r}\)
\(W_{h}\)
\(C_{h}\)
\(\sigma\)
\(\sigma_{h}\)
\(\mathcal{x}\)
\(\mathcal{y}\)
\(\mathcal{x} – \mathcal{y} = 0\)
\(\mathcal{D}_{r}\)
\(\mathcal{x} – \mathcal{yz} \leq \mathcal{D}_{r}\)
(\mathcal{x} – \mathcal{yz} > \mathcal{D}_{r})
$$V_{sphere} = \frac{4}{3}\pi r^3$$
A DORA-CC protocol among \(n\) nodes \(p_1,p_2,\dots,p_n\) with each node having inputs \(v_i\), for a given agreement distance \(\mathcal{D}\), guarantees that:
Given an agreement distance \(\mathcal{D}\), we say that two values \(v_1\) and \(v_2\) agree with each other, if \(|v_1 – v_2| \leq \mathcal{D}\). That is, if two values differ at most by the agreement distance, then they are said to agree with each other.
A set of values \(CC\) is said to form a {\em coherent cluster}, if \(\forall v_1, v_2 \in CC: |v_1 – v_2| \leq \mathcal{D}\). In other words, a coherent cluster is a set of values where all the values in that set agrees amongst themselves.
Let \(S_r\) denote the \(S\)-value of round \(r\). A circuit-breaker function \(\frac{|S_r – S_{r-1}|}{S_{r-1}} \geq thr\) triggers and breaks the circuit (or halts the trade) when \(S_r\) deviates from \(S_{r-1}\) by more than some percentage threshold defined by \(thr\).
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