## Abstract

Read-once functions have gained recent, renewed interest in the fields of theory and algorithms of Boolean functions, computational learning theory and logic design and verification. In an earlier paper [M.C. Golumbic, A. Mintz, U. Rotics, Factoring and recognition of read-once functions using cographs and normality, and the readability of functions associated with partial k-trees, Discrete Appl. Math. 154 (2006) 1465-1677], we presented the first polynomial-time algorithm for recognizing and factoring read-once functions, based on a classical characterization theorem of Gurvich which states that a positive Boolean function is read-once if and only if it is normal and its co-occurrence graph is P_{4}-free. In this note, we improve the complexity bound by showing that the method can be modified slightly, with two crucial observations, to obtain an O (n | f |) implementation, where | f | denotes the length of the DNF expression of a positive Boolean function f, and n is the number of variables in f. The previously stated bound was O (n^{2} k), where k is the number of prime implicants of the function. In both cases, f is assumed to be given as a DNF formula consisting entirely of the prime implicants of the function.

Original language | English |
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Pages (from-to) | 1633-1636 |

Number of pages | 4 |

Journal | Discrete Applied Mathematics |

Volume | 156 |

Issue number | 10 |

DOIs | |

State | Published - 28 May 2008 |

## Keywords

- Boolean functions
- Cographs
- Logic
- Read-once functions

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics