## Abstract

For an arbitrary set B of Boolean functions satisfying a certain condition, we give a general method of constructing a class C_{B} of read-once Boolean formulas over the basis B that has the following property: For any F in CB, F can be transformed to an optimal formula (i.e., a simplest formula over the standard basis {AND,OR,NOT}) by replacing each occurrence of a basis function h ∈ B in F with an optimal formula for h. For a particular set of basis functions B^{*} = {AND,OR,NOT,XOR,MUX}, we give a canonical form representation for C_{B} ^{*} so that the set of canonical form formulas consists of only NPNr epresentatives in C _{B} ^{*}.

Original language | English |
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Pages (from-to) | 1008-1015 |

Number of pages | 8 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E93-A |

Issue number | 6 |

DOIs | |

Publication status | Published - Jan 1 2010 |

## All Science Journal Classification (ASJC) codes

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Electrical and Electronic Engineering