function STRS = dfsa_generate(M,depth)
% generates all strings 
% that are accepted by M in <= depth steps

STRS = {};
Q = M.q0;
S = {''};
DS = deadstates_dfsa(M);
PROGstart(depth,'generating...');
for d=1:depth
  Q1 = [];
  S1 = {};
  for i=1:length(Q)
    q = Q(i);
    u = S{i};
    if ismember(q,M.F)
      STRS{end+1} = u;
    end
    for s=M.ALF
      p = dfsa_delta(M,q,s);
      if ~ismember(p,DS)
        Q1(end+1)=p;
        S1{end+1}=[u s];
      end
    end
  end
  Q=Q1;
  S=S1;
  PROGupdate(d);
end
PROGend;
return