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fixes a notation

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Sanaz 2021-01-13 18:50:17 -08:00
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rln-research/merkle-tree-update.md
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@ -37,7 +37,7 @@ In the solution explained below, we enable a peer to perform the operations desc
The solution relies on the following statement:
> In a Merkle Tree with the capacity of `N` leaves, one can compute the root of the tree by maintaining the root nodes of log(N) number of complete Merkle trees.
We use the preceding observation and define `F = [(L:0, H0, leafIndex0), ..., (L:d, Hd, leafIndexd)]` to be an array of size log(N)+1 holding the root of the complete (left) sub-trees for levels `[0, ..., d=log(N)]`. Each entry of `F` is a tuple `(L, leafIndex, H)` in which `H` is the root of the complete subtree at level `L`, and `leafIndex` indicates the index of the leaf node whose insertion resulted in `H`. The storage of `leafIndex` in each tuple will later enables the efficient support of deletion operation. Each peer shall store `F` locally.
We use the preceding observation and define `F = [(L:0, H0, leafIndex0), ..., (L:d, Hd, leafIndexd)]` to be an array of size log(N)+1 holding the root of the complete (left) sub-trees for levels `[0, ..., d=log(N)]`. Each entry of `F` is a tuple `(L, H, leafIndex)` in which `H` is the root of the complete subtree at level `L`, and `leafIndex` indicates the index of the leaf node whose insertion resulted in `H`. The storage of `leafIndex` in each tuple will later enables the efficient support of deletion operation. Each peer shall store `F` locally.
For the Merkle Tree (with 6 leaves) shown in Figure below, `F` is highlighted in green and has the following value `F = [(L:0, N12, leafIndex:5), (L:1, N6, leafIndex:6), (L:2, N2, leafIndex:4), (L:3, N1, leafIndex:6)]`. Note that `F` only contains the green nodes but none of the gray nodes.