docs: def dfa_complementation(dfa: dict) -> dict:
      """ Returns a DFA that accepts any word but he ones accepted
      by the input DFA.
  
      Let A be a completed DFA, :math:`Ā = (Σ, S, s_0 , ρ, S − F )`
      is the DFA that runs A but accepts whatever word A does not.
  
      :param dict dfa: input DFA.
      :return: *(dict)* representing the complement of the input DFA.
      """
      dfa_complement = dfa_completion(deepcopy(dfa))
      dfa_complement['accepting_states'] = \
          dfa_complement['states'].difference(dfa_complement['accepting_states'])
      return dfa_complement