How to determine if a regex is orthogonal to another regex?

Question

I guess my question is best explained with an (simplified) example.

Regex 1:

^\\d+_[a-z]+$

Regex 2:

^\\d*$
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Answer 1

I would do the following:

• convert each regex to a FSA, using something like the following structure:

  struct FSANode
  {
      bool accept;
      Map<char, FSANode> links;
  }
  List<FSANode> nodes;
  FSANode start;
  

Note that this isn't trivial, but for simple regex shouldn't be that difficult.

• Make a new Combined Node like:

  class CombinedNode
  {
      CombinedNode(FSANode left, FSANode right)
      {
          this.left = left;
          this.right = right;
      }
  
      Map<char, CombinedNode> links;
      bool valid { get { return !left.accept || !right.accept; } }
  
      public FSANode left;
      public FSANode right;
  }
  

Build up links based on following the same char on the left and right sides, and you get two FSANodes which make a new CombinedNode.

Then start at CombinedNode(leftStart, rightStart), and find the spanning set, and if there are any non-valid CombinedNodes, the set isn't "orthogonal."