19. Is the family of deterministic context-free languages closed under
homomorphism?
20. Give the details of the inductive argument in Theorem 8.5.
21. Give an algorithm which, for any given context-free grammar G, can
determine whether or not λ ε L (G).
22. Show that there exists an algorithm to determine whether the language
generated by some context-free grammar contains any words of length less
than some given number n.
23. Let L 1 be a context-free language and L 2 be regular. Show that there exists
an algorithm to determine whether or not L 1 and L 2 have a common element.