## Abstract

We study relationships between the class of Boolean formulas called exclusive-or expansions based on monotone DNF formulas (⊗MDNF formulas, for short) and the class of Horn DNF formulas. An ⊗MDNF formula f is a Boolean formula represented by f = f_{1}⊗ ⋯ ⊗ f_{d}, where f_{1} > ⋯ > f_{d} are monotone DNF formulas and no terms appear more than once. A Horn DNF formula is a DNF formula where each term contains at most one negative literal. We show that the class of double Horn functions, where both f and its negation f̄ can be represented by Horn DNF formulas, coincides with a subclass of ⊗MDNF formulas such that each DNF formula f_{i} consists of a single term. Furthermore, we give an incrementally polynomial time algorithm that transforms a given Horn DNF formula into the ×MDNF representation.

Original language | English |
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Pages (from-to) | 343-351 |

Number of pages | 9 |

Journal | IEICE Transactions on Information and Systems |

Volume | E87-D |

Issue number | 2 |

Publication status | Published - Jan 1 2004 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence