## Abstract

A weighted sequence is a sequence of probability distributions over an alphabet of size σ. Weighted sequences arise naturally in many applications. We study the problem of weighted pattern matching in which we are given a string pattern P of length m, a weight threshold [Formula presented], and a weighted text X arriving on-line. We say that P occurs in X at position i if the product of probabilities of the letters of P at positions i−m+1,…,i in X is at least [Formula presented]. We first discuss how to apply a known general scheme that transforms off-line pattern matching algorithms to on-line algorithms to obtain an on-line algorithm that requires O((σ+logz)logm) or O(σlog^{2}m) time per arriving position; with the space requirement however being O(mmin(σ,z)). Our main result is a new algorithm that processes each arriving position of X in O(z+σ) time using O(m+z) extra space.

Original language | English |
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Pages (from-to) | 49-59 |

Number of pages | 11 |

Journal | INFORMATION AND COMPUTATION |

Volume | 266 |

Early online date | 3 Jan 2019 |

DOIs | |

Publication status | Published - 1 Jun 2019 |

## Keywords

- On-line pattern matching
- Position weight matrix (PWM)
- String matching automaton
- Uncertain sequence
- Weighted sequence