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The shortest disjunctive normal forms of Boolean functions by reducing the number of arguments Yung, Ho Sen
Abstract
Denoting the length of a shortest disjunctive normal form of a Boolean function / by l(f), this thesis provides a way to express l(f) in terms of l(g) for some Boolean function g with no more arguments than f and with the same number of zeros as f . This method is useful for finding the shortest disjunctive normal forms of Boolean functions f with few zeros. It also gives explicitly the values of l(f) for f with three or fewer zeros, and some bounds for l(f) for a certain class of Boolean functions f . For n much larger than k, the zeros of a Boolean function f of n arguments with k zeros have the property that for some large subsets P = {i₁,i₂,…,i[sub d]} of {1,2,..., n} and 1 ≤ c ≤ d, all k zeros s satisfy Si₁ = Si₂ = ... = Si[sub c] = Si[sub c]+1 = Si[sub c]+2 = ... = Si[sub d]. Thus, one may consider all dimensions in each P as a single dimension and construct a corresponding Boolean function g with fewer arguments.
Item Metadata
Title |
The shortest disjunctive normal forms of Boolean functions by reducing the number of arguments
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2002
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Description |
Denoting the length of a shortest disjunctive normal form of a Boolean function /
by l(f), this thesis provides a way to express l(f) in terms of l(g) for some Boolean
function g with no more arguments than f and with the same number of zeros as f .
This method is useful for finding the shortest disjunctive normal forms of Boolean
functions f with few zeros. It also gives explicitly the values of l(f) for f with three
or fewer zeros, and some bounds for l(f) for a certain class of Boolean functions f .
For n much larger than k, the zeros of a Boolean function f of n arguments
with k zeros have the property that for some large subsets P = {i₁,i₂,…,i[sub d]} of
{1,2,..., n} and 1 ≤ c ≤ d, all k zeros s satisfy Si₁ = Si₂ = ... = Si[sub c] = Si[sub c]+1 =
Si[sub c]+2 = ... = Si[sub d]. Thus, one may consider all dimensions in each P as a single
dimension and construct a corresponding Boolean function g with fewer arguments.
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Extent |
1163407 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-08-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0051443
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2002-05
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.