function DFSA = list_all_skel(n,alf)
% enumerates all "skeleton" DFSAs on n states with alphabet alf
% i.e., accepting states don't matter
% this is only for a tiny tiny sanity check, as for alf='ab',
% this is practical only for n<=3; at most 4

DFSA = [];
A = str2dfsa(alf,alf);
Q = 1:n;
nalf = length(alf);

DELTA = list_all_ind(repmat([n],[1 n*nalf]));
DFSA = repmat(A,[size(DELTA,1),1]);

PROGstart(length(DFSA));
cnt = 0;
for di = 1:size(DELTA,1)
  delta = reshape(DELTA(di,:),[n nalf]);
  for q0 = 1
    
    F = [];
    A.ALF = alf;
    A.Q = Q;
    A.q0 = q0;
    A.F = F;
    A.delta = delta;
      
    cnt = cnt + 1;
    DFSA(cnt) = A;
    PROGupdate(cnt);
  end
end
PROGend;

return