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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)

Revision as of 12:33, 10 March 2009

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==Note 14==

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<~~pre~~>

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===Computation Summary : <math>g(u, v) = \texttt{((u,~v))}</math>===

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~~No doubt everybody who's still awake sacrificed~~

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~~the few spare moments of their sleep last night~~

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~~that it took to Figure all this out already~~,

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~~but just for the record here's what I got:~~

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~~Computation Summary for g<u, v> = ((u, v))~~

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Figure 2.1 expands <math>g = \texttt{((u,~v))}</math> over <math>[u, v]\!</math> into the logically equivalent exclusive disjunction: <math>\texttt{uv ~+~ (u)(v)}.</math>

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Figure 2.1 expands g = ((u, v)) over [u, v] into

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the equivalent exclusive disjunction uv + (u)(v).

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<pre>

o---------------------------------------o

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o---------------------------------------o

Figure 2.1. g = ((u, v))

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</pre>

Figure 2.2 expands Eg = ((u + du, v + dv)) over [u, v] to give:

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uv.((du, dv)) + u(v).(du, dv) + (u)v.(du, dv) + (u)(v).((du, dv))

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<pre>

o---------------------------------------o

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o---------------------------------------o

Figure 2.2. Eg = ((u + du, v + dv))

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</pre>

Figure 2.3 expands Dg = g + Eg over [u, v] to yield the form:

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uv.(du, dv) + u(v).(du, dv) + (u)v.(du, dv) + (u)(v).(du, dv)

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<pre>

o---------------------------------------o

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Jon Awbrey

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