The probability of finding a fixed pattern in random data depends monotonically on the bifix indicator

Alex Schreiber

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arXiv · 1207.6991

The probability of finding a fixed pattern in random data depends monotonically on the bifix indicator

Alex Schreiber

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Abstract

We consider the problem of finding a fixed L-ary sequence in a stream of random L-ary data. It is known that the expected search time is a strictly increasing function of the lengths of the bifices of the pattern. In this paper we prove the related statement that the probability of finding the pattern in a finite random word is a strictly decreasing function of the lengths of the bifices of the pattern.

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Alex Schreiber. 2012-07-30. The probability of finding a fixed pattern in random data depends monotonically on the bifix indicator. https://arxiv.org/abs/1207.6991

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