Optimal Parallel Pattern Matching in Strings

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Optimal Parallel Pattern Matching in Strings
U Vishkin
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(Lemma 1 and induction on the number of stages are, again, all that required to prove this. This was referred to as ([log m]-2)-sparsity earlier).
The terminal stage . For each of these three possible zeros, check in a character by character fashion if they stand for a period of the pattern. If not, update WITNESS using (possibly) simultaneous writes into the same memory locations.
Case 1. 2 . PATTERN [ 1, ... , 2 t^°g ^]-^] has a period whose size is P ]-2-i. (That is, if there had been stage
...[log m]-l, it would have started at Box 4). The terminal stage .
for all j, 2t^°g ™]"2

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