Tuesday, September 12, 2006

The potency of configurations

As a fun question to try to answer related to Turing machines... let Cn represent the set of all Turing templates of n states, as defined in the last post. Let P(c) represent the potency of configuration c∈Cn, defined to be the mean productivity of all the Turing machines t∈c.
The question: What's the distribution of P(c)?

Why it matters...

If P(c) has a Gaussian distribution with a fairly tight standard deviation, then the potency function is a useful heuristic that could be used to drive an A* search through Cn. A few samples of t∈c could establish whether c is worth examining.

It's not likely to be the case though, given that two machines in c could behave completely differently. This suggests looking for a different similarity metric between machines.

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