Design a TM to perform circular left-shift operation. Design a TM to accept the language (o,1,2 l a,b 21) Draw the state-transition diagram, and explain how your TM operates 1. 2. 3. Let w 100101 and G be the context-free grammar whose productions are given below (Note that G is in Chomsky Normal Form) 2. SYK . C-YC Draw a parse tree for w Test membership of w in L(G) using CYK algorithm (CYK algorithm is discussed in Section 7.4.4 of the textbook). Write down your solution step by step by giving proper explanations. Which nonterminals in G can be used to generate w? a. b. c. 4. Given language L = {0' 121331 i'jz1) a. Prove that L is context-free b. For a given language X, let Half(X) (wl wx e X and Iw x). Prove that Half(L) is not context free Design a TM to perform circular left-shift operation. Design a TM to accept the language (o,1,2 l a,b 21) Draw the state-transition diagram, and explain how your TM operates 1. 2. 3. Let w 100101 and G be the context-free grammar whose productions are given below (Note that G is in Chomsky Normal Form) 2. SYK . C-YC Draw a parse tree for w Test membership of w in L(G) using CYK algorithm (CYK algorithm is discussed in Section 7.4.4 of the textbook). Write down your solution step by step by giving proper explanations. Which nonterminals in G can be used to generate w? a. b. c. 4. Given language L = {0' 121331 i'jz1) a. Prove that L is context-free b. For a given language X, let Half(X) (wl wx e X and Iw x). Prove that Half(L) is not context free