# LogSpace Merkle Traversal

I am studying LogSpace Merkle Tree Traversal algorithm in this book. In the [pag. 58] I don't understand the Table 1. My question is Why within of the $2^h$ rounds for $NEED_h$ exist only one $TAIL$, if tail in the page 42 is defined than intermediate nodes in $STACK_h$? $STACK_h$ is defined to be an object which contains a stack of node values $STACK_h. initialize$ and $STACK_h.update$ will be methods to setup and incrementally execute treehash.The period starting from the time $STACK_h$ is created and ending at the time when the upcoming authentication node is required to be completed is denoted than $NEED_h$.

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I suggest that you provide a self-contained definition of all mathematical notation and algorithms, in your question, so that people don't have to go look elsewhere to understand what is being asked. –  D.W. Aug 29 at 20:24