## Abstract

In this paper, we present the first polynomial time algorithm for recognizing and factoring read-once functions. The algorithm is based on algorithms for cograph recognition and a new efficient method for checking normality. Its correctness is 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-occurrance graph is P_{4}-free. We also investigate the problem of factoring certain non-read-once functions. In particular, we show that if the co-occurrence graph of a positive Boolean function f is a tree, then the function is read-twice. We then extend this further proving that if f is normal and its corresponding graph is a partial k-tree, then f is a read 2^{k} function and a read 2^{k} formula for F for f can be obtained in polynomial time.

Original language | English |
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Pages (from-to) | 357-361 |

Number of pages | 5 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 22 |

DOIs | |

State | Published - 15 Oct 2005 |

## Keywords

- boolean functions
- cographs
- k-trees
- normal functions
- read-once functions

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics