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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
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, 03:24, 2 March 2009→Note 8: markup
Onward and upward to Flatland, the differential analysis of transformations between 2-dimensional universes of discourse.
Onward and upward to Flatland, the differential analysis of transformations between 2-dimensional universes of discourse.
Consider the transformation from the universe <math>U^\circ = [u, v]</math> to the universe <math>X^\circ = [x, y]</math> that is defined by this system of equations:
Consider the transformation from the universe U% = [u, v] to the
universe X% = [x, y] that is defined by this system of equations:
x = f<u, v> = ((u)(v))
{| align="center" cellpadding="8" width="90%"
| <math>x ~=~ f(u, v) ~=~ \underline{((}~ u ~\underline{)(}~ v ~\underline{))}</math>
|-
| <math>y ~=~ g(u, v) ~=~ \underline{((}~ u ~,~ v ~\underline{))}</math>
|}
The underlined parenthetical expressions on the right are the cactus forms for the boolean functions that correspond to inclusive disjunction and logical equivalence, respectively. By way of a reminder, consult Table 1 on the page at this location:
:* [http://stderr.org/pipermail/inquiry/2003-May/000478.html DLOG D1]
<pre>
The component notation F = <F_1, F_2> = <f, g> : U% -> X% allows
The component notation F = <F_1, F_2> = <f, g> : U% -> X% allows
us to give a name and a type to this transformation, and permits
us to give a name and a type to this transformation, and permits