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===Output===
===Output===
One component of the <math>\begin{smallmatrix}\operatorname{Theme~One}\end{smallmatrix}</math> program that I wrote some years ago finds all the satisfying interpretations of propositions expressed in cactus syntax. It's not a polynomial time algorithm, as you may guess, but it was just barely efficient enough to do this example in the 500 K of spare memory that I had on an old 286 PC in about 1989, so I will give you the actual outputs from those trials.
One component of the Theme One program that I wrote some years ago
finds all the satisfying interpretations of propositions expressed
in cactus syntax. It's not a polynomial time algorithm, as you may
guess, but it was just barely efficient enough to do this example
in the 500 K of spare memory that I had on an old 286 PC in about
1989, so I will give you the actual outputs from those trials.
Output Conditions for Tape Input "0"
====Output Conditions for Tape Input "0"====
<pre>
Let P_0 be the proposition that we get by conjoining
Let P_0 be the proposition that we get by conjoining
the proposition that describes the initial conditions
the proposition that describes the initial conditions
the tape head H if and when the machine M reaches one of
the tape head H if and when the machine M reaches one of
its resting states, we get the result that Parity(0) = 0.
its resting states, we get the result that Parity(0) = 0.
</pre>
Output Conditions for Tape Input "1"
====Output Conditions for Tape Input "1"====
<pre>
Let P_1 be the proposition that we get by conjoining
Let P_1 be the proposition that we get by conjoining
the proposition that describes the initial conditions
the proposition that describes the initial conditions
