min(Not Closed) ex- {L = { $a^{i}b^{j}c^{k}$ | k= min(i,j), i,j,k>0 }}
max(Not Closed) ex- {L = { $a^{i}b^{j}c^{k}$ | k= max(i,j), i,j,k>0 }}
half(Not Closed)
ex- Let L = { $a^{n} b^{n} c^{i} dd^{3i}d$ | n>0, i>0 } Since CFL is closed under intersection with regular languages, we can do half(L) ∩ a*b*c*d which splits L into two halves: $a^{n} b^{n} c^{i} d$ and $ d^{3i}d$ In order for these to be of equal length, i = n, So half(L) ∩ a*b*c*d = $a^{n} b^{n} c^{n} d$, which we know is not a CFL.
alt(Not Closed)
ex - ( If w = a1a2....an and x = b1b2....bm and y= c1c2c3.......cl are strings of the same length, define alt(w,x,y) to be the string in which the symbols of w,x and y alternate, starting with w, that is a1b1c1a2b2c2....anbmcl).
init(closed)
cylcle(closed)
I/a (no idea what is this)
set difference(not closed)