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

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of <math>9 + 12 + 36 = 57\!</math> basic propositions or boolean variables:
 
of <math>9 + 12 + 36 = 57\!</math> basic propositions or boolean variables:
   −
  p0_r0, p0_r1, p0_r2,
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{| align="center" cellpadding="8" width="90%"
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  p1_r0, p1_r1, p1_r2,
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|
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  p2_r0, p2_r1, p2_r2.
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<math>\begin{matrix}
 +
\texttt{p0\_r0}, & \texttt{p0\_r1}, & \texttt{p0\_r2},
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\\[6pt]
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\texttt{p1\_r0}, & \texttt{p1\_r1}, & \texttt{p1\_r2},
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\\[6pt]
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\texttt{p2\_r0}, & \texttt{p2\_r1}, & \texttt{p2\_r2}.
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\end{matrix}</math>
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|}
   −
  p0_q#, p0_q*, p0_q0, p0_q1,
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{| align="center" cellpadding="8" width="90%"
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  p1_q#, p1_q*, p1_q0, p1_q1,
+
|
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  p2_q#, p2_q*, p2_q0, p2_q1.
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<math>\begin{matrix}
 +
\texttt{p0\_q\#}, & \texttt{p0\_q*}, & \texttt{p0\_q0}, & \texttt{p0\_q1},
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\\[6pt]
 +
\texttt{p1\_q\#}, & \texttt{p1\_q*}, & \texttt{p1\_q0}, & \texttt{p1\_q1},
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\\[6pt]
 +
\texttt{p2\_q\#}, & \texttt{p2\_q*}, & \texttt{p2\_q0}, & \texttt{p2\_q1}.
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\end{matrix}</math>
 +
|}
   −
  p0_r0_s#, p0_r0_s*, p0_r0_s0, p0_r0_s1,
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{| align="center" cellpadding="8" width="90%"
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  p0_r1_s#, p0_r1_s*, p0_r1_s0, p0_r1_s1,
+
|
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  p0_r2_s#, p0_r2_s*, p0_r2_s0, p0_r2_s1,
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<math>\begin{matrix}
 +
\texttt{p0\_r0\_s\#}, & \texttt{p0\_r0\_s*}, & \texttt{p0\_r0\_s0}, & \texttt{p0\_r0\_s1},
 +
\\[4pt]
 +
\texttt{p0\_r1\_s\#}, & \texttt{p0\_r1\_s*}, & \texttt{p0\_r1\_s0}, & \texttt{p0\_r1\_s1},
 +
\\[4pt]
 +
\texttt{p0\_r2\_s\#}, & \texttt{p0\_r2\_s*}, & \texttt{p0\_r2\_s0}, & \texttt{p0\_r2\_s1},
 +
\\[12pt]
 +
\texttt{p1\_r0\_s\#}, & \texttt{p1\_r0\_s*}, & \texttt{p1\_r0\_s0}, & \texttt{p1\_r0\_s1},
 +
\\[4pt]
 +
\texttt{p1\_r1\_s\#}, & \texttt{p1\_r1\_s*}, & \texttt{p1\_r1\_s0}, & \texttt{p1\_r1\_s1},
 +
\\[4pt]
 +
\texttt{p1\_r2\_s\#}, & \texttt{p1\_r2\_s*}, & \texttt{p1\_r2\_s0}, & \texttt{p1\_r2\_s1},
 +
\\[12pt]
 +
\texttt{p2\_r0\_s\#}, & \texttt{p2\_r0\_s*}, & \texttt{p2\_r0\_s0}, & \texttt{p2\_r0\_s1},
 +
\\[4pt]
 +
\texttt{p2\_r1\_s\#}, & \texttt{p2\_r1\_s*}, & \texttt{p2\_r1\_s0}, & \texttt{p2\_r1\_s1},
 +
\\[4pt]
 +
\texttt{p2\_r2\_s\#}, & \texttt{p2\_r2\_s*}, & \texttt{p2\_r2\_s0}, & \texttt{p2\_r2\_s1}.
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\end{matrix}</math>
 +
|}
   −
  p1_r0_s#, p1_r0_s*, p1_r0_s0, p1_r0_s1,
+
This means that the propositional program itself is nothing more or less than a single proposition or boolean function <math>p : \mathbb{B}^{57} \to \mathbb{B}.</math>
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  p1_r1_s#, p1_r1_s*, p1_r1_s0, p1_r1_s1,
  −
  p1_r2_s#, p1_r2_s*, p1_r2_s0, p1_r2_s1,
  −
 
  −
  p2_r0_s#, p2_r0_s*, p2_r0_s0, p2_r0_s1,
  −
  p2_r1_s#, p2_r1_s*, p2_r1_s0, p2_r1_s1,
  −
  p2_r2_s#, p2_r2_s*, p2_r2_s0, p2_r2_s1.
  −
 
  −
This means that the propositional program itself is nothing more or less than a single proposition or a boolean function <math>p : \mathbb{B}^{57} \to \mathbb{B}.</math>
      
<pre>
 
<pre>
Jon Awbrey
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