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nkohen committed Feb 2, 2021
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Expand Up @@ -16,7 +16,7 @@ protection against unresponsive and otherwise corrupted oracles.
Using multiple oracles also provides a better environment for contract updates to a new oracle should
one of the oracles being used announce that it will become unresponsive or has lost control of its keys.

A key feature of this proposal is that no change in behavior is required of oracles when compared to
A key feature of this proposal is that no change in behavior is required of oracles when compared to
single-oracle DLCs.
All work is done by DLC participants using existing DLC oracles as they are.

Expand All @@ -26,7 +26,7 @@ the same events.
The majority of this document, however, is devoted to treating the numeric case where oracles are allowed
to have bounded disagreements.

In any of these cases, using multiple oracles does introduce a multiplier on total the number of CETs.
In any of these cases, using multiple oracles does introduce a multiplier on the total number of CETs.
In general, this multiplier grows exponentially with the number of oracles, but remains low enough
for small numbers of oracles to enable the most common use cases (2-of-3 and 3-of-5) without much trouble.
Larger numbers of oracles can still be used in cases where they are needed, but the CET cost incurred may be large.
Expand All @@ -51,8 +51,8 @@ Larger numbers of oracles can still be used in cases where they are needed, but
## Multiple Oracles for Enumerated Outcome Events

In the case of enumerated outcome events, where there is no macroscopic structure to the set of
CETs and all oracles of a given event are expected to sign the same outcomes, then there is little
work to do to support multiple oracles.
CETs and all oracles of a given event are expected to sign the same outcomes, little work is required
to support multiple oracles.

The n-of-n case is accomplished by simple point addition in the same manner as is done to combine
multiple digit signatures in numeric outcome DLCs from digit decomposition.
Expand Down Expand Up @@ -87,7 +87,7 @@ To construct a DLC for an enumerated outcome event using some threshold t-of-n o
we construct CETs for all outcomes for all possible combinations of t-of-t oracles.

For example, say there are three oracles, Olivia, Oren, and Ollivander, who will be attesting
two one of two outcomes, A or B.
to one of two outcomes, A or B.
If we wish to construct a 2-of-3 DLC over these outcomes using these oracles, we will construct
and adaptor sign a total of 6 CETs:

Expand Down Expand Up @@ -224,7 +224,7 @@ This discarding is the primary opinion decidedly made from the design space by t
leads to better guarantees at the expense of more CETs.
The resulting CET(s) can then either be used (in the case of maximize coverage) or shrunk until they cover as little as
possible while still containing `[start - minFail, end + minFail]` by repeatedly cutting them in half on either side.
This process results in 1-3 secondary oracle CETs for ever single CET of the primary oracle.
This process results in 1 to 3 secondary oracle CETs for ever single CET of the primary oracle (see [algorithm below](#algorithm)).

### 2-of-2 Oracles with Bounded Error

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