As I said in my earlier comment, the initial configurations should be restricted to ones that extend only over a finite region. Such configurations are countable and the halting problem for them satisfies your criteria.

I think the set of all finite subsets is the better choice for a domain here. For one, it is countable. But also, when your starting configurations extend out infinitely, there is no hope to begin with of computing their fate.

@Joseph: not that I know of.

For real-time preview latex software, you might find some ideas here: stackoverflow.com/questions/311118/real-time-latex

duplicate of mathoverflow.net/questions/104906

I wonder if transcendental numbers qualify here. Does anybody know the history?

Glad to know I'm not the only one who gives serious thought to the trade-off between security and laziness in scrambling my bike lock. In fact, I have arrived at a similar conclusion as others here have: if I always scramble to the same position, I get more security for same laziness than if I scramble same number of positions randomly.

There is no general way, but perhaps you can use one of the "theorems of the alternative" such as Farkas's Lemma, Gale's Theorem, etc.

Why do you expect any peculiarities? One subgroup I know whose order is $O(N^2)$ is the Weyl-Heisenberg group generated by the two maps $|k\rangle\mapsto |k+1\rangle$ and $|k\rangle\mapsto e^{2\pi k/N}|k\rangle$, where $|k\rangle$, $k=0,\ldots, N-1 \pmod{N}$, is a orthonormal basis of $\mathbb C^N$.

I used to think that T stood for Tikhonov.

This reference might be useful: springerlink.com/content/u744kkug4563q3lp

Is this significantly different than asking for the family of graphs that are contact graphs of arbitrary convex solids?

What's wrong with picking one of the Gaussians w/prob proportional to their weight and sampling from it (all repeated $d$ times)? Why do you need a better way?