SUBTREE ISOMORPHISM

• One way we could reduce complexity is to optimize the number of states in a deterministic finite state automaton. If we exploit the tree structure of the graph, we can do more aggressive optimization.
  
  
• Two subtrees are said to be isomorphic to each other if they can be made equivalent by permuting the successors.
  
  
• Similarly, two states are indistinguishable if and only if their subtrees are isomorphic.
  
  
• We can merge subtrees that are isomorphic within a lexical tree. There are automated algorithms to do this.