Are there any good / interesting analogs to regular expressions in 2d?

Question

Are there any good (or at least interesting but flawed) analogs to regular expressions in two dimensions?

In one dimension I can write something like /aaac?(bc)*b?

Answer 1

Nice problem.

First, ask yourself if you can constrain the pattern to a "+" pattern, or if you would it need to test/match rectangles also. For instance, a rectangle of [bc] with a border of a would match the center rectangle below, but would also match a "+" shape of [c([bc]*a})v([bc]*a)>([bc]*a)<([bc]*a)] (in your syntax)

xxxaaaaaxxx
yzyabcba12d
defabcbass3
oreabcba3s3
s33aaaaas33
k388x.egiee

If you can constrain it to a "+" then your task is much easier. As ShuggyCoUk said, parsing a RE is usually equivalent to a DFSM -- but for a single, serial input which simplifies things greatly.

In your "RE+" engine, you'll have to debug not only the engine, but also each place that the expressions are entered. I'd like the compiler to catch any errors it could. Given that, you could also use something that was explicitly four RE's, like:

REPlus engine = new REPlus('b').North("a{3}")
   .East("a{3}").South("a{3}").West("a{3}");

However, depending on your implementation this may be cumbersome.

And with regard to the traversal engine -- would the North/West patterns match RtL or LtR? It could matter if the patterns match differently with or w/o greedy sub-matches.

Incidentally, I think the '^' in your example is supposed to be one character to the left, outside the parenthesis.