function [b,A,C,dd] = is_markov(P,m,n)
% is the distribution P over S^n a Markov one?
% that is, is P(X(t)|X(1:t-1)) = P(X(t)|X(t-1))?
% if yes, returns the Markov kernels A

tol = 1e-8;

A = pnormdim(ones(m,m,n-1),1);
C = pnormdim(ones(m,1,  1),1);

dd = [];

b = 1;
for t=2:n
  prefdim = repmat([m],[1 t-1]);
  for ipref = 1:m^(t-1)
    long = ind2coord(ipref,prefdim);
    shrt = long(end);
    plong = getPX(P,m,n,long,1:t-1) + realmin;
    pshrt = getPX(P,m,n,shrt,  t-1) + realmin;
    for Xt = 1:m
      pjlong = getPX(P,m,n,[long Xt],  1:t);
      pjshrt = getPX(P,m,n,[shrt Xt],t-1:t);      
      full = pjlong / plong;
      part = pjshrt / pshrt;
      %if abs(full-part) > tol
      %  b = 0;
      %  dif = abs(full-part)
      %  return
      %end
      dd(end+1) = abs(full-part);
      %if dd(end)>.01
      %  keyboard
      %end
      A(Xt,shrt,t-1) = full;
    end
  end
end

% compute the initial prob C
for x1 = 1:m
  C(x1) = getPX(P,m,n,x1,1);
end

b = (max(dd)<tol);

return