function M = randlt(alf,minidlen,maxidlen,minnumids,maxnumids)
% outputs a random locally testable language
% by computing a random boolean function of random shuffle ideals
% minidlen = minimal ideal length
% maxidlen = maximal ideal length (smaller => simpler language)
% minnumids = minimal total of ideals in the number boolean expression
% maxnumids) = maximal number of ideals (smaller => simpler language)

S = {};
MM = {};
numids = round(randinseg(minnumids,maxnumids));
for i=1:numids
  u = get_datum_unique(alf,minidlen,maxidlen,S)
  S{i} = u;
  %if isempty(u)
  %  u = '@';
  %end
  fprintf('processing U = %s \n',u);
  % just do n-grams
  M = midl2dfsa(u,alf);
  if 0
    r = rand;
    if r<1/3
      % prefix
      M = pref2dfsa(u,alf);
    elseif r<2/3
      % suffix
      M = suff2dfsa(u,alf);
    else
      % inside
      M = midl2dfsa(u,alf);
    end
  end
  MM{i} = M;
end

ii = randperm(numids);
ii=ii(:)';
M = MM{ii(1)};
if flip
  M = negate_fsa(M);
end
for i=ii(2:end)
  Mi = MM{i};
  if flip
    Mi = negate_fsa(Mi);
  end
  if flip
    M = union_dfsa(M,Mi);
  else
    M = intersect_dfsa(M,Mi);
  end
end

% as a bit of clean-up:
% a loc-test language never contains the empty string:
M = intersect_dfsa(M,negate_fsa(str2dfsa('',alf)));
return


function r = randinseg(a,b)
r = rand*(b-a) + a;
return

function b=flip
b = round(rand);
return

function x = get_datum_unique(alf,minidlen,maxidlen,PREV)
good = 0;
na = length(alf);
while ~good
  n = round(randinseg(minidlen,maxidlen));
  x = alf(ceil(rand(1,n)*na));
  good = isempty(strmatch(x,PREV,'exact'));
end
return