a) Consider the following Context Free Grammar G ((A, B, C), (a, $), P, S):

P:

S AB | BC

A BA |CCA| a

B CC |$

C AB | a

Using CYK algorithm find out whether the string a$a$ is a member of the language L(G) or not?

b) Consider the following Context Free Grammar G ((A, B, C), (x, -), P, S):

P:

S AB | BC

A BA | x

B CC |ABC| -

C AB | x

String x-x-x is a member of the language L(G). Is the statement True or False? Justify your answer with the help of CYK algorithm.