English

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

Probability 2012-07-31 v1 Information Theory math.IT

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.

Keywords

Cite

@article{arxiv.1207.6991,
  title  = {The probability of finding a fixed pattern in random data depends monotonically on the bifix indicator},
  author = {Alex Schreiber},
  journal= {arXiv preprint arXiv:1207.6991},
  year   = {2012}
}

Comments

7 pages

R2 v1 2026-06-21T21:43:30.807Z