### Abstract

This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

Original language | English |
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Pages (from-to) | 234-251 |

Number of pages | 18 |

Journal | Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) |

Volume | 3194 |

Publication status | Published - Jan 1 2004 |

Event | 14th International Conference ILP 2004: Inductive Logic Programming - Porto, Portugal Duration: Sep 6 2004 → Sep 8 2004 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**An efficient algorithm for reducing clauses based on constraint satisfaction techniques.** / Maloberti, Jérôme; Suzuki, Einoshin.

Research output: Contribution to journal › Conference article

*Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)*, vol. 3194, pp. 234-251.

}

TY - JOUR

T1 - An efficient algorithm for reducing clauses based on constraint satisfaction techniques

AU - Maloberti, Jérôme

AU - Suzuki, Einoshin

PY - 2004/1/1

Y1 - 2004/1/1

N2 - This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

AB - This paper presents a new reduction algorithm which employs Constraint Satisfaction Techniques for removing redundant literals of a clause efficiently. Inductive Logic Programming (ILP) learning algorithms using a generate and test approach produce hypotheses with redundant literals. Since the reduction is known to be a co-NP-complete problem, most algorithms are incomplete approximations. A complete algorithm proposed by Gottlob and Fermüller is optimal in the number of θ-subsumption calls. However, this method is inefficient since it exploits neither the result of the θ-subsumption nor the intermediary results of similar θ-subsumption calls. Recently, Hirata has shown that this problem is equivalent to finding a minimal solution to a θ-subsumption of a clause with itself, and proposed an incomplete algorithm based on a θ-subsumption algorithm of Scheffer. This algorithm has a large memory consumption and performs many unnecessary tests in most cases. In this work, we overcome this problem by transforming the θ-subsumption problem in a Constraint Satisfaction Problem, then we use an exhaustive search algorithm in order to find a minimal solution. The experiments with artificial and real data sets show that our algorithm outperforms the algorithm of Gottlob and Fermüller by several orders of magnitude, particularly in hard cases.

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UR - http://www.scopus.com/inward/citedby.url?scp=22944444187&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:22944444187

VL - 3194

SP - 234

EP - 251

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -