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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 03:36, 14 March 2009
, 03:36, 14 March 2009→Note 23: markup
==Note 23==
==Note 23==
Given but a single free square on the tape, there are just two different sets of initial conditions for <math>\operatorname{Stunt}(2),</math> the finite approximation to the parity turing machine that we are presently considering.
Given but a single free square on the tape, there are just
two different sets of initial conditions for Stunt(2), the
finite approximation to the parity turing machine that we
are presently considering.
===Initial Conditions for Tape Input "0"===
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "0" in its free square:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{l}
\texttt{p0\_q0}
\\ \\
\texttt{p0\_r1}
\\ \\
\texttt{p0\_r0\_s\#}
\\
\texttt{p0\_r1\_s0}
\\
\texttt{p0\_r2\_s\#}
\end{array}</math>
|}
This conjunction of basic propositions may be read as follows:
This conjunction of basic propositions may be read as follows:
<pre>
At time p_0, M is in the state q_0, and
At time p_0, M is in the state q_0, and
At time p_0, H is reading cell r_1, and
At time p_0, H is reading cell r_1, and
At time p_0, cell r_1 contains "0", and
At time p_0, cell r_1 contains "0", and
At time p_0, cell r_2 contains "#".
At time p_0, cell r_2 contains "#".
</pre>
Initial Conditions for Tape Input "1"
===Initial Conditions for Tape Input "1"===
The following conjunction of 5 basic propositions
The following conjunction of 5 basic propositions describes the initial conditions when <math>\operatorname{Stunt}(2)</math> is started with an input of "1" in its free square:
describes the initial conditions when Stunt(2) is
started with an input of "1" in its free square:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{l}
\texttt{p0\_q0}
\\ \\
\texttt{p0\_r1}
\\ \\
\texttt{p0\_r0\_s\#}
\\
\texttt{p0\_r1\_s1}
\\
\texttt{p0\_r2\_s\#}
\end{array}</math>
|}
This conjunction of basic propositions may be read as follows:
This conjunction of basic propositions may be read as follows:
<pre>
At time p_0, M is in the state q_0, and
At time p_0, M is in the state q_0, and
At time p_0, H is reading cell r_1, and
At time p_0, H is reading cell r_1, and