function M2 = reassign_alf_dfsa(M1,ALF2,MAP)
% remap the alphabet of M1 to the new letters ALF2
% applying the MAP transformation
% (not necessarily a one-to-one transformation)
% M1.ALF, ALF2, MAP  must all have same length

% if MAP contains '@' then these characters are simply consumed
% actually, I'm not sure how to deal with '@' so I'll leave it for later
% OK, here's how we deal with '@': its preimage is a dead letter
% meaning that if it's observed, we reject!

l(1) = length(M1.ALF);
l(2) = length(ALF2);
l(3) = length(MAP);
if ~all(l==l(1))
  error('M1.ALF, ALF2, MAP  must all have same length');
end

M2 = M1;
M2.ALF = ALF2;

nQ1 = length(M1.Q);

% deadlets cause all states to transit to dead state
deadlets = setdiff(ALF2,MAP);
dl = ~isempty(deadlets);

nQ2 = nQ1+dl;	% create an extra dead state for the dead letters
M2.Q = 1:nQ2;
M2 = init_ddelta(M2);

if dl
  for s=deadlets
    M2 = set_ddelta(M2,M2.Q(1:end-1),repmat(s,[1,nQ1]),repmat(nQ2,[1,nQ1]));
  end
  % dead state transits to itself on all letters
  M2 = set_ddelta(M2,repmat(nQ2,[1,length(M2.ALF)]),M2.ALF,repmat(nQ2,[1,length(M2.ALF)]));
end



%PROGstart(nQ1*length(M1.ALF),'reassigning alphabet...')
%cnt = 0;
for q=M1.Q
  for si=1:length(M1.ALF)
    s = M1.ALF(si);
    r = dfsa_delta(M1,q,s);
    t = ALF2(si);
    t1 = MAP(si);
    %if (t1=='@')
    %  % just consume t
    %  M2 = set_ddelta(M2,q,t,q);
    %else
      M2 = set_ddelta(M2,q,t1,r);
    %end
    %cnt = cnt + 1;
    %PROGupdate(cnt);
  end
end
%PROGend;


%M2 = minimize_dfsa(M2);
return