I'm only just starting to learn about the PCP, and I'm especially interested in the Bounded version. From Wikipedia:
One of the most important variants of PCP is the bounded Post correspondence problem, which asks if we can find a match using no more than k tiles, including repeated tiles.
I am not sure I understand what Wiki means by a 'tile' in this context.
I do understand that a typical PCP problem takes as input two equal-length lists of nonempty strings, each of which contains some number of words. An example is this:
M = (abb, aa, aaa) and
N = (bba, aaa, aa)
In terms of the Bounded PCP, what would the integer K be here? Is it the length an individual word can be (which in this case is maxed at 3)? Is it the length of a single list?
Hope this is clear. I appreciate any help profusely in advance.