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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 20:37, 9 March 2009
, 20:37, 9 March 2009→Note 13: \texttt
A sketch of this work is presented in the following series of Figures, where each logical proposition is expanded over the basic cells <math>\texttt{uv}, \texttt{u(v)}, \texttt{(u)v}, \texttt{(u)(v)}</math> of the 2-dimensional universe of discourse <math>U^\circ = [u, v].\!</math>
A sketch of this work is presented in the following series of Figures, where each logical proposition is expanded over the basic cells <math>\texttt{uv}, \texttt{u(v)}, \texttt{(u)v}, \texttt{(u)(v)}</math> of the 2-dimensional universe of discourse <math>U^\circ = [u, v].\!</math>
===Computation Summary for <math>f(u, v) = \texttt{((u)(v))}</math>===
===Computation Summary : <math>f(u, v) = \texttt{((u)(v))}</math>===
Figure 1.1 is a venn diagram that show how the proposition <math>f = \texttt{((u)(v))}</math> can be expanded over the universe of discourse <math>[u, v]\!</math> to produce a logically equivalent exclusive disjunction, namely, <math>\texttt{uv~+~u(v)~+~(u)v}.</math>
Figure 1.1 is a venn diagram that show how the proposition <math>f = \texttt{((u)(v))}</math> can be expanded over the universe of discourse <math>[u, v]\!</math> to produce a logically equivalent exclusive disjunction, namely, <math>\texttt{uv~+~u(v)~+~(u)v}.</math>
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Figure 1.2 expands Ef = ((u + du)(v + dv)) over [u, v] to give:
Figure 1.2 expands <math>\operatorname{E}f = \texttt{((u + du)(v + dv))}</math> over <math>[u, v]\!</math> to give:
uv.(du dv) + u(v).(du (dv)) + (u)v.((du) dv) + (u)(v).((du)(dv))
{| align="center" cellpadding="8" width="90%"
| <math>\texttt{uv~(du~dv) ~+~ u(v)~(du (dv)) ~+~ (u)v~((du) dv) ~+~ (u)(v)~((du)(dv))}</math>
|}
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