diff --git a/regexp.py b/regexp.py
--- a/regexp.py
+++ b/regexp.py
@@ -332,10 +332,31 @@ class RegexpDFA:
 					queue.append(sj)
 			rules.extend(index[sj] for sj in row)
 		
-		end_states = {index[si] for si in self.end_states}
+		end_states = {index[si] for si in self.end_states if si in index}
 
 		return RegexpDFA(rules, end_states, self.alphabet_index)
 
+	def find_distinguishing_string(self, r):
+		if self.rules == r.rules and self.end_states == r.end_states:
+			return None
+
+		product = self._build_product_automaton(r)
+
+		n = len(product.alphabet_index)
+		reverse_alphabet_index = {v: k for (k, v) in product.alphabet_index.items()}
+		queue = deque([(0, "")])
+		visited = {0}
+		while queue:
+			(state, acc) = queue.popleft()
+			if state in product.end_states:
+				return acc
+			for (i, target) in enumerate(product.rules[state*n:(state+1)*n]):
+				if target not in visited:
+					queue.append((target, acc+reverse_alphabet_index[i]))
+					visited.add(target)
+		
+		assert False
+
 	def _find_equivalent_states(self):
 		n = len(self.alphabet_index)
 		state_list = list(range(len(self.rules) // n))
@@ -380,6 +401,24 @@ class RegexpDFA:
 		
 		return (rules, end_states)
 
+	def _build_product_automaton(self, r):
+		n = len(self.alphabet_index)
+		m = len(r.rules) // n
+		k = len(self.rules) // n
+
+		rules = []
+		end_states = set()
+
+		for s1 in range(k):
+			row1 = self.rules[s1*n:(s1+1)*n]
+			for s2 in range(m):
+				row2 = r.rules[s2*n:(s2+1)*n]
+				rules.extend([x*m + y for (x, y) in zip(row1, row2)])
+				if (s1 in self.end_states) != (s2 in r.end_states):
+					end_states.add(s1*m + s2)
+
+		return RegexpDFA(rules, end_states, self.alphabet_index).reduce().normalize()
+
 
 def test():
 	tests = ["", "a", "ab", "aabb", "abab", "abcd", "abcbcdbcd"]
@@ -408,6 +447,11 @@ if __name__ == "__main__":
 	match_parser.add_argument("string")
 	match_parser.set_defaults(name="match")
 
+	compare_parser = subparsers.add_parser("compare")
+	compare_parser.add_argument("pattern1")
+	compare_parser.add_argument("pattern2")
+	compare_parser.set_defaults(name="compare")
+
 	args = parser.parse_args()
 
 	if args.name == "test":
@@ -419,5 +463,9 @@ if __name__ == "__main__":
 			print("Failed to parse the regexp:")
 			print(e)
 		print(r.match(args.string))
+	elif args.name == "compare":
+		r1 = RegexpDFA.create(args.pattern1).reduce().normalize()
+		r2 = RegexpDFA.create(args.pattern2).reduce().normalize()
+		print(r1.find_distinguishing_string(r2))
 	else:
-		parser.print_help()
\ No newline at end of file
+		parser.print_help()