Spring , 2013 CIS 511 Introduction to the Theory of Computation

Hint . Without loss of generality, assume that L = L(G), where G = (V,Σ, P, S) is in Chomsky normal form, and let R = L(D), for some DFA D = (Q,Σ, δ, q0, F ). Use a kind of cross-product construction as sketched below. Construct a CFG G2 whose set of nonterminals is Q×N ×Q ∪ {S0}, where S0 is a new nonterminal, and whose productions are of the form: S0 → (q0, S, f), for every f ∈ F ; (p,A, δ(p, a))→ a iff (A→ a) ∈ P, for all a ∈ Σ, all A ∈ N , and all p ∈ Q;