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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 18:32, 15 March 2009
, 18:32, 15 March 2009→Interpretation of the Propositional Program: markup
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In the interpretation of the cactus language for propositional logic that we are using here, an expression of the form <math>\texttt{(p(q))}</math> expresses a ''conditional'', an ''implication'', or an ''if-then'' proposition, commonly read in one of the following ways:
In the interpretation of the cactus language for propositional logic
that we are using here, an expression of the form "(p (q))" expresses
{| align="center" cellpadding="8" width="90%"
a conditional, an implication, or an if-then proposition, commonly read
|
<math>\begin{array}{l}
\operatorname{not}~ p ~\operatorname{without}~ q
\\[4pt]
p ~\operatorname{implies}~ q
\\[4pt]
\operatorname{if}~ p ~\operatorname{then}~ q
\\[4pt]
p \Rightarrow q
\end{array}</math>
|}
A text string expression of the form "(p (q))" corresponds
A text string expression of the form <math>\texttt{(p(q))}</math> corresponds to a graph-theoretic data-structure of the following form:
to a graph-theoretic data-structure of the following form:
<pre>
o---------------------------------------o
o---------------------------------------o
| |
| |
| ( p ( q )) |
| ( p ( q )) |
o---------------------------------------o
o---------------------------------------o
</pre>
Taken together, the Mediate Conditions state the following:
Taken together, the Mediate Conditions state the following:
<pre>
If M at p_0 is in state q_#, then M at p_1 is in state q_#, and
If M at p_0 is in state q_#, then M at p_1 is in state q_#, and
If M at p_0 is in state q_*, then M at p_1 is in state q_*, and
If M at p_0 is in state q_*, then M at p_1 is in state q_*, and