Consider the language L_1 = (a" b" i m. n > 0) Construct a context free grammar such that L(G) = L_1 Construct a regular grammar G such that L(G) = L_1 Consider the language L_2 = (a" b" i n > 0) Construct a context-free grammar G such that L(G) = L_x, Explain why there cannot exist a regular grammar G Such that L(G) = L_2 Determine L_1, U L_2 L, L_2 L_1*. and L_2*. where L_1 and L_2 are as defined above Give a regular grammar that generates ma strings over (a. b. c) in which the as precede the. which in turn precede the It is possible mat there are no a's. b's. or c's Consider the grammar G with production rules S rightarrow BSA I A A rightarrow aA| lambda 8 rightarrow Bba I lambda Construction an equivalent essentially non-contracting grammar. i.e., there are no production rules of the form V rightarrow lambda. except S rightarrow lambda if lambda in L(G)) and with a non-recursive start symbol Hint tee section 4 .2 and the examples Give a regular expression tor the language L(G) where G is the grammar is question 7