### Abstract

An elementary formal system (EFS) is a logic program consisting of definite clauses whose arguments have patterns instead of first-order terms. We investigate EFSs for polynomial-time PAC-learnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pattern in the head. With this new notion, we show that H-EFS(m, k, t, r) is polynomial-time learnable, which is the class of languages definable by EFSs consisting of at most m hereditary definite clauses with predicate symbols of arity at most r, where k and t bound the number of variable occurrences in the head and the number of atoms in the body, respectively. The class defined by all finite unions of EFSs in H-EFS(m, k, t, r) is also polynomial-time learnable. We also show an interesting series of NC-learnable classes of EFSs. As hardness results, the class of regular pattern languages is shown not polynomial-time learnable unless RP = NP. Furthermore, the related problem of deciding whether there is a common subsequence which is consistent with given positive and negative examples is shown NP-complete.

Original language | English |
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Pages | 217-242 |

Number of pages | 26 |

Volume | 18 |

No. | 3 |

Specialist publication | New Generation Computing |

DOIs | |

Publication status | Published - 2000 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications

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## Cite this

*New Generation Computing*,

*18*(3), 217-242. https://doi.org/10.1007/BF03037530