function M0 = minimize_dfsa(M0)
% M1 is the smallest equivalent dfsa to M0
% see str2dfsa.m for basic dfsa definitions

nQ = length(M0.Q);
% the brute-force, debug version

% initialize the \equiv_0 relation
EQU = zeros(nQ);
for p=1:nQ
  for q=p+1:nQ
    Mp = M0; Mp.q0 = p;
    Mq = M0; Mq.q0 = q;    
    EQU(p,q) = equal_dfsa(Mp,Mq);
  end
end

% collapse equivalent states
for p=1:nQ
  for q=p+1:nQ
    if EQU(p,q)
      M0 = collapse(M0,p,q);
    end
  end
end
M0 = remove_unreachable(M0);
return


function M = collapse(M,p,q)
% everything that pointed to q must point to p

[qq0,ss0] = get_ddparents(M,q);
M = set_ddelta(M,qq0,ss0,repmat(p,[length(qq0),1]));
% now just zero out q:
M = set_ddelta(M,repmat(q,[length(M.ALF) 1]),M.ALF,zeros(length(M.ALF),1));

% take q out of F if it's there
M.F = setdiff(M.F,q);
return