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taproot – Question about MAST tree in book “mastering bitcoin”

Moussa by Moussa
March 2, 2024
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It seems to me that the text should read “we could also have four conditions for the same cost”.

MAST is a binary tree, which means the number of possible scripts (conditions) grows exponentially with the size of the inclusion proof, or equivalently, the size of the inclusion proof grows logarithmically with the number of possible scripts. For example, in a balanced tree:

  • 1 commitment (merkle root) gives you 1 possible script
  • 2 commitments (merkle root and 1 branch step) give you 2 possible scripts
  • 3 commitments (merkle root and 2 branch steps) give you 4 possible scripts
  • 4 commitments (merkle root and 3 branch steps) give you 8 possible scripts

What the original text is saying that 3 and 4 possible scripts both require 3 commitments.

It’s important to note (and the very next section in the book goes over this) that using an imperfect/unbalanced binary tree can be beneficial if you expect some of the conditions to be used more often. By putting these shallower in the tree you use less block space on average.



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