code: def valid?
        # @todo Check that each state is connected.
        #   Iterate through each states to verify the graph
        #   is not disjoint.
        @transitions.each do |key, val|
          @alphabet.each do |a| 
            return false unless @transitions[key].has_key? a.to_s
          end
        end
        return true
      end
docs: Verifies that the initialized DFA is valid.
   Checks that each state has a transition for each
   symbol in the alphabet.
  
   @return [Boolean] whether or not the DFA is valid.