Changes

MyWikiBiz, Author Your Legacy — Tuesday November 19, 2024
Jump to navigationJump to search

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

Revision as of 02:48, 20 March 2009

1,308 bytes added ,  02:48, 20 March 2009
→‎Output Conditions for Tape Input "1": markup
Line 2,629: Line 2,629:     
====Output Conditions for Tape Input "1"====
 
====Output Conditions for Tape Input "1"====
 +
 +
Let <math>p_1\!</math> be the proposition that we get by conjoining the proposition that describes the initial conditions for tape input "1" with the proposition that describes the truncated turing machine <math>\operatorname{Stunt}(2).</math>  As it turns out, <math>p_1\!</math> has a single satisfying interpretation.  This interpretation is expressible in the form of a singular proposition, which can in turn be indicated by its positive logical features, as shown in the following display:
 +
 +
<br>
    
<pre>
 
<pre>
−
Let P_1 be the proposition that we get by conjoining
  −
the proposition that describes the initial conditions
  −
for tape input "1" with the proposition that describes
  −
the truncated turing machine Stunt(2).  As it turns out,
  −
P_1 has a single satisfying interpretation, and this is
  −
represented as a singular proposition in terms of its
  −
positive logical features in the following display:
  −
   
o-------------------------------------------------o
 
o-------------------------------------------------o
 
|                                                |
 
|                                                |
Line 2,658: Line 2,654:  
|                                                |
 
|                                                |
 
o-------------------------------------------------o
 
o-------------------------------------------------o
 +
</pre>
 +
 +
<br>
    
The Output Conditions for Tape Input "1" can be read as follows:
 
The Output Conditions for Tape Input "1" can be read as follows:
   −
  At the time p_0, M is in the state q_0, and
+
{| align="center" cellpadding=8" width="90%"
−
  At the time p_0, H is reading cell r_1, and
+
|
−
  At the time p_0, cell r_0 contains "#", and
+
<p>At the time <math>p_0,\!</math> machine <math>\operatorname{M}</math> is in the state <math>q_0,\!</math> and</p>
−
  At the time p_0, cell r_1 contains "1", and
+
<p>At the time <math>p_0,\!</math> scanner <math>\operatorname{H}</math> is reading cell <math>r_1,\!</math> and</p>
−
  At the time p_0, cell r_2 contains "#", and
+
<p>At the time <math>p_0,\!</math> cell <math>r_0\!</math> contains the symbol <math>\texttt{\#},</math> and</p>
−
 
+
<p>At the time <math>p_0,\!</math> cell <math>r_1\!</math> contains the symbol <math>\texttt{1},</math> and</p>
−
  At the time p_1, M is in the state q_1, and
+
<p>At the time <math>p_0,\!</math> cell <math>r_2\!</math> contains the symbol <math>\texttt{\#},</math> and</p>
−
  At the time p_1, H is reading cell r_2, and
+
|-
−
  At the time p_1, cell r_0 contains "#", and
+
|
−
  At the time p_1, cell r_1 contains "1", and
+
<p>At the time <math>p_1,\!</math> machine <math>\operatorname{M}</math> is in the state <math>q_1,\!</math> and</p>
−
  At the time p_1, cell r_2 contains "#", and
+
<p>At the time <math>p_1,\!</math> scanner <math>\operatorname{H}</math> is reading cell <math>r_2,\!</math> and</p>
−
 
+
<p>At the time <math>p_1,\!</math> cell <math>r_0\!</math> contains the symbol <math>\texttt{\#},</math> and</p>
−
  At the time p_2, M is in the state q_*, and
+
<p>At the time <math>p_1,\!</math> cell <math>r_1\!</math> contains the symbol <math>\texttt{1},</math> and</p>
−
  At the time p_2, H is reading cell r_1, and
+
<p>At the time <math>p_1,\!</math> cell <math>r_2\!</math> contains the symbol <math>\texttt{\#},</math> and</p>
−
  At the time p_2, cell r_0 contains "#", and
+
|-
−
  At the time p_2, cell r_1 contains "1", and
+
|
−
  At the time p_2, cell r_2 contains "#".
+
<p>At the time <math>p_2,\!</math> machine <math>\operatorname{M}</math> is in the state <math>q_*,\!</math> and</p>
 +
<p>At the time <math>p_2,\!</math> scanner <math>\operatorname{H}</math> is reading cell <math>r_1,\!</math> and</p>
 +
<p>At the time <math>p_2,\!</math> cell <math>r_0\!</math> contains the symbol <math>\texttt{\#},</math> and</p>
 +
<p>At the time <math>p_2,\!</math> cell <math>r_1\!</math> contains the symbol <math>\texttt{1},</math> and</p>
 +
<p>At the time <math>p_2,\!</math> cell <math>r_2\!</math> contains the symbol <math>\texttt{\#}.</math></p>
 +
|}
   −
The output of Stunt(2) being the symbol that rests under
+
The output of <math>\operatorname{Stunt}(2)</math> being the symbol that rests under the tape head <math>\operatorname{H}</math> when and if the machine <math>\operatorname{M}</math> reaches one of its resting states, we get the result that <math>\operatorname{Parity}(1) = 1.</math>
−
the tape head H when and if the machine M reaches one of
  −
its resting states, we get the result that Parity(1) = 1.
  −
</pre>
      
==Work Area==
 
==Work Area==
Jon Awbrey
12,080

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/82866"

Navigation menu