1. Let L = {b$^m$ u$^h$ b$^k$ l$^n$ e$^f$ where n, h >= 0, f>=1, f= m, and 2n = k}
a. Construct a PDA with empty stack that recognizes the strings of L. (20 points)
b. Convert the generated empty-stack PDA into a final-state PDA using the approach studied in lectures. (15 points)
c. Does the word bubble belong to L? Justify your answer with a sequence of moves of the final-state PDA and explain its indication. (15 points)
NOTE: Add the formal description of each one of the above grammars or PDA.