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Wacky Math Formula Test

January 15, 2021 - 1 min read

Testing the appearance of math formulas in search of bugs.


\(\frac{f_{c} + 1}{2}\)





\(2f_{c} + 1\)

\(f_{c} + 1\)

\(r + 1\)


\(2f_{d} + 1\)

\(f_{d} + 1\)



\(2f_{t} + 1\)

\(2f + 1\)

\(f_{t} + 1\)


\(3f_{t} + 1\)









\(\mathcal{x} – \mathcal{y} = 0\)


\(\mathcal{x} – \mathcal{yz} \leq \mathcal{D}_{r}\)

(\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:

  1. [Termination] : All honest nodes eventually agree on some value.
  2. [Agreement] : The output value \(\mathcal{S}\) for all the nodes is the same.
  3. [Validity] : \(H_{min} – \mathcal{D} \leq \mathcal{S} \leq H_{max}\), where \(H_{min}\) and \(H_{max}\) denote the minimum and maximum values from honest nodes.

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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