### The potency of configurations

As a fun question to try to answer related to Turing machines... let

*C*represent the set of all Turing templates of_{n}*n*states, as defined in the last post. Let*P(c)*represent the*potency*of configuration*c∈C*, defined to be the mean productivity of all the Turing machines_{n}*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 C_{n}. 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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