OT For you math junkies

I can almost follow along with most of the math discussed around here but this just makes me feel dumb. It's a math problem that has just recently been solved that has had mathmeticians stumped for the last 30 years.

http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.0099v4.pdf

I didn't know there was a road coloring problem!!! Where have I been?

allscott said:

I can almost follow along with most of the math discussed around here but this just makes me feel dumb. It's a math problem that has just recently been solved that has had mathmeticians stumped for the last 30 years.

http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.0099v4.pdf

Click to expand...

Does this mean we can expect to have more colorful roads in the future? The article assume you are already tuned into authors 'geek freq'. There are many terms that aren't defined. Few even know the difference between a graph and a tree. In this case a graph is not like a trend and a tree is not something you sit under for shade.

I don't claim to be a mathametician, but I've had a little abstract math and automata theory. The author is uses standard math and computer science terminology - that's not to say it isn't a beast to follow!

What they're doing is constructing conditions for a specific type of state machine so that it has a special input sequence that will bring it back to the same state from every state.

Image a soda machine that accepted nickles, dimes, and quarters. Each finite state represents some amount of money in the machine. If you didn't have a "reset", you could construct it so that feeding a "NDDNDDNDD" always gets you to the initial state (no money).

Better analogy based on Wikipedia example - suppose on the road you always have 3 choices (straight, right, left). Your friend could give you a set of directions that would get you home from any location. Note that some paths would probably pass your home at least once, but all would get you there.

They state that this is useful for a state machine because, upon detection of an error, a sequence could be fed that would return the device to an initial state.

That said, advanced math is knarly and makes my head spin.

allscott said:

I can almost follow along with most of the math discussed around here but this just makes me feel dumb. It's a math problem that has just recently been solved that has had mathmeticians stumped for the last 30 years.

http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.0099v4.pdf

Click to expand...