Relationships between Horn Formulas and XOR-MDNF Formulas

Kenshi Matsuo, Tetsuya Koyama, Eiji Takimoto, Akira Maruoka

Research output: Contribution to journalArticle

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 = 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.

Original languageEnglish
Pages (from-to)343-351
Number of pages9
JournalIEICE Transactions on Information and Systems
VolumeE87-D
Issue number2
Publication statusPublished - Jan 1 2004
Externally publishedYes

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Polynomials

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: IEICE Transactions on Information and Systems, Vol. E87-D, No. 2, 01.01.2004, p. 343-351.

Research output: Contribution to journalArticle

Matsuo, K, Koyama, T, Takimoto, E & Maruoka, A 2004, 'Relationships between Horn Formulas and XOR-MDNF Formulas', IEICE Transactions on Information and Systems, vol. E87-D, no. 2, pp. 343-351.
Matsuo, Kenshi ; Koyama, Tetsuya ; Takimoto, Eiji ; Maruoka, Akira. / Relationships between Horn Formulas and XOR-MDNF Formulas. In: IEICE Transactions on Information and Systems. 2004 ; Vol. E87-D, No. 2. pp. 343-351.
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