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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 15:32, 19 March 2009
, 15:32, 19 March 2009→Output Conditions for Tape Input "0": markup
====Output Conditions for Tape Input "0"====
====Output Conditions for Tape Input "0"====
Let <math>p_0\!</math> be the proposition that we get by conjoining the proposition that describes the initial conditions for tape input "0" with the proposition that describes the truncated turing machine <math>\operatorname{Stunt}(2).</math> As it turns out, <math>p_0\!</math> has a single satisfying interpretation, and this is represented as a singular proposition in terms of its positive logical features in the following display:
<br>
<pre>
<pre>
o-------------------------------------------------o
o-------------------------------------------------o
| |
| |
| |
| |
o-------------------------------------------------o
o-------------------------------------------------o
</pre>
<br>
The Output Conditions for Tape Input "0" can be read as follows:
The Output Conditions for Tape Input "0" can be read as follows:
At the time p_2, cell r_2 contains "#".
At the time p_2, cell r_2 contains "#".
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> if and when the machine <math>\operatorname{M}</math> reaches one of its resting states, we get the result that <math>\operatorname{Parity}(0) = 0.</math>
the tape head H if and when the machine M reaches one of
its resting states, we get the result that Parity(0) = 0.
</pre>
====Output Conditions for Tape Input "1"====
====Output Conditions for Tape Input "1"====