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

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{| align="center" cellpadding="8" width="90%"
 
{| align="center" cellpadding="8" width="90%"
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| At the point-in-time <math>p_i,\!</math> the finite state machine <math>\operatorname{M}</math> is in the state <math>q_j.\!</math></p>
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| At the point-in-time <math>p_i,\!</math> the finite state machine <math>\operatorname{M}</math> is in the state <math>q_j.\!</math>
 
|}
 
|}
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|}
 
|}
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<pre>
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The proposition of the form <math>\texttt{pi\_rj}</math> says:
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The proposition of the form pi_rj says:
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  At the point-in-time p_i,
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{| align="center" cellpadding="8" width="90%"
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  the tape-head H is on the tape-cell r_j.
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| At the point-in-time <math>p_i,\!</math> the tape head <math>\operatorname{H}</math> is on the tape cell <math>r_j.\!</math>
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|}
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The basic propositions for describing the
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The basic propositions for describing the ''present symbol function'' <math>\operatorname{SF} : P \to (R \to S)</math> are these:
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"present symbol function" SF : P -> (R -> S)
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are these:
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  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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|
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  p0_r2_s#, p0_r2_s*, p0_r2_s0, p0_r2_s1,
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<math>\begin{matrix}
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  p0_r3_s#, p0_r3_s*, p0_r3_s0, p0_r3_s1,
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\texttt{p0\_r0\_s\#}, & \texttt{p0\_r0\_s*}, & \texttt{p0\_r0\_s0}, & \texttt{p0\_r0\_s1},
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  p1_r0_s#, p1_r0_s*, p1_r0_s0, p1_r0_s1,
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\\[4pt]
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  p1_r1_s#, p1_r1_s*, p1_r1_s0, p1_r1_s1,
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\texttt{p0\_r1\_s\#}, & \texttt{p0\_r1\_s*}, & \texttt{p0\_r1\_s0}, & \texttt{p0\_r1\_s1},
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  p1_r2_s#, p1_r2_s*, p1_r2_s0, p1_r2_s1,
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\\[4pt]
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  p1_r3_s#, p1_r3_s*, p1_r3_s0, p1_r3_s1,
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\texttt{p0\_r2\_s\#}, & \texttt{p0\_r2\_s*}, & \texttt{p0\_r2\_s0}, & \texttt{p0\_r2\_s1},
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  p2_r0_s#, p2_r0_s*, p2_r0_s0, p2_r0_s1,
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\\[4pt]
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  p2_r1_s#, p2_r1_s*, p2_r1_s0, p2_r1_s1,
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\texttt{p0\_r3\_s\#}, & \texttt{p0\_r3\_s*}, & \texttt{p0\_r3\_s0}, & \texttt{p0\_r3\_s1},
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  p2_r2_s#, p2_r2_s*, p2_r2_s0, p2_r2_s1,
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\\[4pt]
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  p2_r3_s#, p2_r3_s*, p2_r3_s0, p2_r3_s1,
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\texttt{p1\_r0\_s\#}, & \texttt{p1\_r0\_s*}, & \texttt{p1\_r0\_s0}, & \texttt{p1\_r0\_s1},
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  p3_r0_s#, p3_r0_s*, p3_r0_s0, p3_r0_s1,
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\\[4pt]
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  p3_r1_s#, p3_r1_s*, p3_r1_s0, p3_r1_s1,
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\texttt{p1\_r1\_s\#}, & \texttt{p1\_r1\_s*}, & \texttt{p1\_r1\_s0}, & \texttt{p1\_r1\_s1},
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  p3_r2_s#, p3_r2_s*, p3_r2_s0, p3_r2_s1,
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\\[4pt]
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  p3_r3_s#, p3_r3_s*, p3_r3_s0, p3_r3_s1.
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\texttt{p1\_r2\_s\#}, & \texttt{p1\_r2\_s*}, & \texttt{p1\_r2\_s0}, & \texttt{p1\_r2\_s1},
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\\[4pt]
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\texttt{p1\_r3\_s\#}, & \texttt{p1\_r3\_s*}, & \texttt{p1\_r3\_s0}, & \texttt{p1\_r3\_s1},
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\\[4pt]
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\texttt{p2\_r0\_s\#}, & \texttt{p2\_r0\_s*}, & \texttt{p2\_r0\_s0}, & \texttt{p2\_r0\_s1},
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\\[4pt]
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\texttt{p2\_r1\_s\#}, & \texttt{p2\_r1\_s*}, & \texttt{p2\_r1\_s0}, & \texttt{p2\_r1\_s1},
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\\[4pt]
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\texttt{p2\_r2\_s\#}, & \texttt{p2\_r2\_s*}, & \texttt{p2\_r2\_s0}, & \texttt{p2\_r2\_s1},
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\\[4pt]
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\texttt{p2\_r3\_s\#}, & \texttt{p2\_r3\_s*}, & \texttt{p2\_r3\_s0}, & \texttt{p2\_r3\_s1},
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\\[4pt]
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\texttt{p3\_r0\_s\#}, & \texttt{p3\_r0\_s*}, & \texttt{p3\_r0\_s0}, & \texttt{p3\_r0\_s1},
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\\[4pt]
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\texttt{p3\_r1\_s\#}, & \texttt{p3\_r1\_s*}, & \texttt{p3\_r1\_s0}, & \texttt{p3\_r1\_s1},
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\\[4pt]
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\texttt{p3\_r2\_s\#}, & \texttt{p3\_r2\_s*}, & \texttt{p3\_r2\_s0}, & \texttt{p3\_r2\_s1},
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\\[4pt]
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\texttt{p3\_r3\_s\#}, & \texttt{p3\_r3\_s*}, & \texttt{p3\_r3\_s0}, & \texttt{p3\_r3\_s1},
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\\[4pt]
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\end{matrix}</math>
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|}
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The proposition of the form pi_rj_sk says:
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The proposition of the form <math>\texttt{pi\_rj\_sk}</math> says:
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  At the point-in-time p_i,
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{| align="center" cellpadding="8" width="90%"
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  the tape-cell r_j bears the mark s_k.
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| At the point-in-time <math>p_i,\!</math> the tape cell <math>r_j\!</math> bears the mark <math>s_k.\!</math>
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</pre>
      
==Note 23==
 
==Note 23==
Jon Awbrey
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