IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Discrete Mathematics and Its Applications
NPN-Representatives of a Set of Optimal Boolean Formulas
Hideaki FUKUHARAEiji TAKIMOTOKazuyuki AMANO
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2010 Volume E93.A Issue 6 Pages 1008-1015

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Abstract

For an arbitrary set B of Boolean functions satisfying a certain condition, we give a general method of constructing a class CB 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 hB 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 CB* so that the set of canonical form formulas consists of only NPN-representatives in CB*.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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