### Abstract

The learnability of the class of exclusive-or expansion based on monotone DNF formulas is investigated. The class consists of the formulas of the form (Formula presented), where (Formula presented) are monotone DNF formulas. It is shown that any Boolean function can be represented as an formula in this class, and that the representation in the simplest form is unique. Learning algorithms that learn such formulas using various queries are presented: An algorithm with subset and superset queries and one with membership and equivalence queries are given. The former can learn any formula in the class, while the latter is proved to learn formulas of bounded depth, i.e., formulas represented as exclusive-or of a constant number of monotone DNF formulas. In spite of seemingly strong restriction of the depth being constant, the class of formulas of bounded depth includes functions with very high complexity in terms of DNF and CNF representations, so the latter algorithm could learn Boolean functions significantly complex otherwise represented.

Original language | English |
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Title of host publication | Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings |

Editors | Setsuo Arikawa, Arun K. Sharma |

Publisher | Springer Verlag |

Pages | 12-25 |

Number of pages | 14 |

ISBN (Print) | 3540618635, 9783540618638 |

Publication status | Published - Jan 1 1996 |

Externally published | Yes |

Event | 7th International Workshop on Algorithmic Learning Theory, ALT 1996 - Sydney, Australia Duration: Oct 23 1996 → Oct 25 1996 |

### 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 | 1160 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Workshop on Algorithmic Learning Theory, ALT 1996 |
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Country | Australia |

City | Sydney |

Period | 10/23/96 → 10/25/96 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings*(pp. 12-25). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1160). Springer Verlag.