diff --git a/lib/imbecile.rb b/lib/imbecile.rb
index 0c6529b..87fb486 100644
--- a/lib/imbecile.rb
+++ b/lib/imbecile.rb
@@ -1,3 +1,5 @@
+require "erb"
+require "set"
 require_relative "imbecile/cli"
 require_relative "imbecile/grammar"
 require_relative "imbecile/regex"
@@ -5,7 +7,6 @@ require_relative "imbecile/regex/dfa"
 require_relative "imbecile/regex/nfa"
 require_relative "imbecile/regex/unit"
 require_relative "imbecile/version"
-require "erb"
 
 module Imbecile
 
diff --git a/lib/imbecile/regex/dfa.rb b/lib/imbecile/regex/dfa.rb
index 53db7e9..cbdefa1 100644
--- a/lib/imbecile/regex/dfa.rb
+++ b/lib/imbecile/regex/dfa.rb
@@ -4,6 +4,34 @@ module Imbecile
     class DFA
 
       def initialize(nfas)
+        start_nfa = NFA.new
+        nfas.each do |nfa|
+          start_nfa.start_state.add_transition(nil, nfa.start_state)
+        end
+        nil_transition_states = nil_transition_states(start_nfa.start_state)
+      end
+
+      private
+
+      # Determine the set of states that can be reached by nil transitions
+      # from the given state.
+      #
+      # @return [Set<NFA::State>]
+      #   Set of states.
+      def nil_transition_states(state)
+        states = Set[state]
+        analyze_state = lambda do |state|
+          state.transitions.each do |range, dest_state|
+            if range.nil?
+              unless states.include?(dest_state)
+                states << dest_state
+                analyze_state[dest_state]
+              end
+            end
+          end
+        end
+        analyze_state[state]
+        states
       end
 
     end
diff --git a/lib/imbecile/regex/nfa.rb b/lib/imbecile/regex/nfa.rb
index c115692..fbbbe55 100644
--- a/lib/imbecile/regex/nfa.rb
+++ b/lib/imbecile/regex/nfa.rb
@@ -6,6 +6,7 @@ module Imbecile
       class State
 
         attr_accessor :accepts
+        attr_reader :transitions
 
         def initialize
           @transitions = []