### Abstract

A pattern is a finite string of constant and variable symbols. For k≥1, we denote by kμΠ the set of all patterns in which each variable symbol occurs at most ktimes. In particular, we abbreviate μΠ for k=1. The language L(π) of a pattern πis the set of all strings obtained by substituting any non-null constant string for each variable symbol in π. In this paper, we show that any pattern π ∈ kμΠ is exactly identifiable in O(¦ω¦^{k+2}) time from one positive example w ∈ L(π) using ¦ω¦^{k+1}+¦π¦^{k} membership queries. Moreover, we introduce the notion of critical pattern, and show that the number of membership queries can be reduced to ¦ω¦+¦π¦ if the target pattern π∈μΠ is not critical. For instance, any patternπ∈μΠ whose constant parts are of length at most 3 is not critical. Finally, we show a nontrivial subclass of μΠ that is identified using membership queries only, without any initial positive example.

Original language | English |
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Title of host publication | Computational Learning Theory - 3rd European Conference, EuroCOLT 1997, Proceedings |

Editors | Shai Ben-David |

Publisher | Springer-Verlag |

Pages | 185-197 |

Number of pages | 13 |

ISBN (Print) | 3540626859, 9783540626855 |

Publication status | Published - 1997 Jan 1 |

Externally published | Yes |

Event | 3rd European Conference on Computational Learning Theory, EuroCOLT 1997 - Jerusalem, Israel Duration: 1997 Mar 17 → 1997 Mar 19 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1208 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd European Conference on Computational Learning Theory, EuroCOLT 1997 |
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Country | Israel |

City | Jerusalem |

Period | 97/3/17 → 97/3/19 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computational Learning Theory - 3rd European Conference, EuroCOLT 1997, Proceedings*(pp. 185-197). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1208). Springer-Verlag.