1. (10 points) Consider the language (a) Here's an informal description of a PDA recognizing L Read symbols from the input. As each a is read, push it onto the stack. As soon as bs are seen, pop an a off the stack for each b read. If the stack becomes empty, start pushing bs to it as we read them. As soon as as are seen, pop a b off the stack for each a read. If we reach the end of the string and the stack is empty, accept. If the as are finished while the stack still contains bs, or if any more bs appear in the input following this second sequence of as, reject the input Draw its state diagram in JFLAP and include the image in your submission. No justification necessary for this part. (b) A CFG generating L is G = ({S,T.T2},{a, b), R, S) where the set of rules is given by Write out two derivations for the string aabbba, one of which is leftmost and one of which is not. Is the grammar G ambiguous? Justify your answers for this part