### Abstract

In this paper, we extend patterns, introduced by Angluin [Ang80b], to typed patterns by introducing types into variables. A type is a recursive language and a variable of the type is substituted only with an element in the recursive language. This extension enhances the expressive power of patterns with preserving their good properties. First, we give a general learnability result for typed pattern languages. We show that if a class of types has finite elasticity then the typed pattern language is identifiable in the limit from positive data. Next, we give a useful tool to show the conservative learnability of typed pattern languages. That is, if an indexed family L of recursive languages has recursive finite thickness and the equivalence problem for L is decidable, then L is conservatively learnable from positive data. Using this tool, we consider the following classes of types: (1) the class of all strings over subsets of the alphabet, (2) the class of all untyped pattern languages, and (3) a class of ĸ-bounded regular languages. We show that each of these typed pattern languages is conservatively learnable from positive data.

Original language | English |
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Title of host publication | Computational Learning Theory - 2nd European Conference, EuroCOLT 1995, Proceedings |

Editors | Paul Vitanyi |

Publisher | Springer Verlag |

Pages | 367-379 |

Number of pages | 13 |

ISBN (Print) | 9783540591191 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

Externally published | Yes |

Event | 2nd European Conference on Computational Learning Theory, EuroCOLT 1995 - Barcelona, Spain Duration: 1995 Mar 13 → 1995 Mar 15 |

### 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 | 904 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd European Conference on Computational Learning Theory, EuroCOLT 1995 |
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Country | Spain |

City | Barcelona |

Period | 95/3/13 → 95/3/15 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Computational Learning Theory - 2nd European Conference, EuroCOLT 1995, Proceedings*(pp. 367-379). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 904). Springer Verlag. https://doi.org/10.1007/3-540-59119-2_192