### Abstract

The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n, where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.

Original language | English |
---|---|

Title of host publication | Language and Automata Theory and Applications - Third International Conference, LATA 2009, Proceedings |

Publisher | Springer Verlag |

Pages | 422-433 |

Number of pages | 12 |

ISBN (Print) | 9783642009815 |

DOIs | |

Publication status | Published - Jan 1 2009 |

Event | 3rd International Conference on Language and Automata Theory and Applications, LATA 2009 - Tarragona, Spain Duration: Apr 2 2009 → Apr 8 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 5457 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Conference on Language and Automata Theory and Applications, LATA 2009 |
---|---|

Country | Spain |

City | Tarragona |

Period | 4/2/09 → 4/8/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Language and Automata Theory and Applications - Third International Conference, LATA 2009, Proceedings*(pp. 422-433). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5457). Springer Verlag. https://doi.org/10.1007/978-3-642-00982-2_36

**Counting parameterized border arrays for a binary alphabet.** / I, Tomohiro; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Language and Automata Theory and Applications - Third International Conference, LATA 2009, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5457, Springer Verlag, pp. 422-433, 3rd International Conference on Language and Automata Theory and Applications, LATA 2009, Tarragona, Spain, 4/2/09. https://doi.org/10.1007/978-3-642-00982-2_36

}

TY - GEN

T1 - Counting parameterized border arrays for a binary alphabet

AU - I, Tomohiro

AU - Inenaga, Shunsuke

AU - Bannai, Hideo

AU - Takeda, Masayuki

PY - 2009/1/1

Y1 - 2009/1/1

N2 - The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n, where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.

AB - The parameterized pattern matching problem is a kind of pattern matching problem, where a pattern is considered to occur in a text when there exists a renaming bijection on the alphabet with which the pattern can be transformed into a substring of the text. A parameterized border array (p-border array) is an analogue of a border array of a standard string, which is also known as the failure function of the Morris-Pratt pattern matching algorithm. In this paper we present a linear time algorithm to verify if a given integer array is a valid p-border array for a binary alphabet. We also show a linear time algorithm to compute all binary parameterized strings sharing a given p-border array. In addition, we give an algorithm which computes all p-border arrays of length at most n, where n is a a given threshold. This algorithm runs in time linear in the number of output p-border arrays.

UR - http://www.scopus.com/inward/record.url?scp=67649999065&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649999065&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-00982-2_36

DO - 10.1007/978-3-642-00982-2_36

M3 - Conference contribution

AN - SCOPUS:67649999065

SN - 9783642009815

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 422

EP - 433

BT - Language and Automata Theory and Applications - Third International Conference, LATA 2009, Proceedings

PB - Springer Verlag

ER -