code: def dfa_completion(dfa: dict) -> dict:
      
      dfa['states'].add('sink')
      for state in dfa['states']:
          for action in dfa['alphabet']:
              if (state, action) not in dfa['transitions']:
                  dfa['transitions'][state, action] = 'sink'
      return dfa
docs: Side effects on input! Completes the DFA assigning to
      each state a transition for each letter in the alphabet (if
      not already defined).
  
      We say that a DFA is complete if its transition function
      :math:`ρ:S×Σ→S` is a total function, that is,
      for all :math:`s ∈ S` and all :math:`a ∈ Σ` we have that
      exists a :math:`ρ(s,a)=s_x` for some :math:`s_x ∈ S`.
      Given an arbitrary DFA A, its completed version :math:`A_T`
      is obtained as follows:
      :math:`A_T = (Σ, S ∪ \{sink\}, s_0 , ρ_T , F )` with
      :math:`ρ_T(s,a)=sink`
      when :math:`ρ(s,a)` is not defined in A and :math:`ρ_T=ρ` in
      the other cases.
  
      :param dict dfa: input DFA.
      :return: *(dict)* representing the completed DFA.