Self doubt

Question

Say L1 and L2 are cfl , is L1 Ex-or L2 is cfl or not?

Comments

here L1 ex or L2 is (L1 U L2) - (L1 ∩ L2) but CFLs are not closed under intersection so we will not necessarily get a CFL for EX-OR.

---

Xor(a, b) =`ab+ab` here a, b both are cfls, as cfls are not closed under complement so move (a`) to csl again csl. Cfl =csl

Answer 1

L1 exor L2=L1.complement(L2) +complement(L1). L2

here given L1 & L2 are Cfl

L1 & L2 cfl is not closed under complementation

Every cfl is csl

csl is closed under complementation

therefore answer is not cfl