### 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 |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*IEICE Transactions on Information and Systems*,

*E87-D*(2), 343-351.

**Relationships between Horn Formulas and XOR-MDNF Formulas.** / Matsuo, Kenshi; Koyama, Tetsuya; Takimoto, Eiji; Maruoka, Akira.

Research output: Contribution to journal › Article

*IEICE Transactions on Information and Systems*, vol. E87-D, no. 2, pp. 343-351.

}

TY - JOUR

T1 - Relationships between Horn Formulas and XOR-MDNF Formulas

AU - Matsuo, Kenshi

AU - Koyama, Tetsuya

AU - Takimoto, Eiji

AU - Maruoka, Akira

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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 = f1⊗ ⋯ ⊗ fd, where f1 > ⋯ > fd 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 fi consists of a single term. Furthermore, we give an incrementally polynomial time algorithm that transforms a given Horn DNF formula into the ×MDNF representation.

AB - 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 = f1⊗ ⋯ ⊗ fd, where f1 > ⋯ > fd 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 fi consists of a single term. Furthermore, we give an incrementally polynomial time algorithm that transforms a given Horn DNF formula into the ×MDNF representation.

UR - http://www.scopus.com/inward/record.url?scp=1442314945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1442314945&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1442314945

VL - E87-D

SP - 343

EP - 351

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 2

ER -