(a) [5 points] The final state PDA D recognizes the language L shown below. Give the execution trace (sequence of IDs) showing that input aabbccc is in D(L). L {abc {a,b, c) *li, j, k> 0^i=j} , Zolzo a, Zlazo a, alaa b, ale b, c, Zolzo E, ZoZo S ASIA AOA 1 B 1 BOB 0 O (b) [10 points] Design a PDA that recognizes the language below: L-{(01) 2 (0, 1,2}*i, j>0} (c) [10 points) Convert the CFG G shown below into a PDA that accepts L(G) by empty stack and give the execution trace (sequence of IDs) showing that input 01001 is in L(G). 4 (d) [10 points] Using the PDA of part(a) as a starting point, design a final, state PDA that recognizes the language I. shown below. Do you think you could construct a non-ambiguous CFG for language L? Justify your answer. L-labe (a,b,cli,j.k> 0A(i-jvi-k)}