Algorithm 3. Membership query M Q(w).

Input: a word w

Output: true if w is accepted, otherwise false

1: matrix set = γw(w)

2: if matrix_set == null then

3:  return false

4: end if

5: yes = 0, no = 0

6: for matrix in matrix_set do

7:  if $\mathcal{N}$ (matrix) then

8:   yes++

9:  else

10:   no++

11:  end if

12: end for

13: return yes >= no