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Revision as of 17:48, 17 March 2009
, 17:48, 17 March 2009→Interaction Conditions: markup
In briefest terms, the Interaction Conditions simply express the circumstance that the mark on a tape cell cannot change between two points in time unless the tape head is over the cell in question at the initial one of those points in time. All that we have to do is to see how they manage to say this.
In briefest terms, the Interaction Conditions simply express the circumstance that the mark on a tape cell cannot change between two points in time unless the tape head is over the cell in question at the initial one of those points in time. All that we have to do is to see how they manage to say this.
Consider a cactus expression of the following form:
Consider a cactus expression of the following form:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{l}
\texttt{((}~ p_i\_r_j ~\texttt{)}~ p_i\_r_j\_s_k ~\texttt{(}~ p_{i+1}\_r_j\_s_k ~\texttt{))}
\end{array}</math>
|}
This expression has the corresponding cactus graph:
This expression has the corresponding cactus graph:
<pre>
o---------------------------------------o
o---------------------------------------o
| |
| |
| |
| |
o---------------------------------------o
o---------------------------------------o
</pre>
A propositional expression of this form can be read as follows:
A propositional expression of this form can be read as follows:
<pre>
IF:
IF:
At the time p<i+1>, the tape cell r<j> bears the mark s<k>.
At the time p<i+1>, the tape cell r<j> bears the mark s<k>.
</pre>
The eighteen clauses of the Interaction Conditions simply impose
The eighteen clauses of the Interaction Conditions simply impose one such constraint on symbol changes for each combination of the times <math>p_0, p_1,\!</math> registers <math>r_0, r_1, r_2,</math> and symbols <math>s_0, s_1, s_\#.\!</math>
one such constraint on symbol changes for each combination of the
times p_0, p_1, registers r_0, r_1, r_2, and symbols s_0, s_1, s_#.
</pre>
===Transition Relations===
===Transition Relations===
