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2. (10 points) A clean Turing machine (cTM) is defined to be a Turing machine which satisfies the ad- ditional constraint that, at the end of each accepting computation, the tape is empty (i.e. all cells are blank) In this problem, you'll show that every Turing machine is equivalent to a clean Turing machine. To describe your construction, you'll first demonstrate how it works on an example, and then write out the general case formally a. Consider the Turing machine over the alphabet 2 0,1 given by the state diagram (using the usual conventions listed in Problem 1) 1:1,R 0:0,R 1:0,R q0 ac Draw the state diagram of a clean Turing machine that is equivalent to this one in JFLAP, export the image as a png or jpg file, and include it as part of your submission. You may use the standard conventions (like in Problem 1) for drawing state diagrams You do not need to justify your construction for credit, but if you describe how your state diagram works by explaining the role of each state and transition, we may be able to award partial credit if your answer is incorrect. b. Consider an arbitrary Turing machine M-Q. ? ?, ?,90,gacc ,grej). Define a clean Turing machine M' such that L(M) - L(M') by giving precise (but general) definitions for each parameter in the formal definition of M,-(2,,2, ?,, ,,96, qacc.4ej) For the purpose of your construction, you may assume that (D) to a non-blank cell of the tape. You do not need to justify your construction for credit, but if you describe how your construction works with an implementation-level description, we may be able to award partial credit if your answer is incorrect M does not ever write a blank symbol 2. (10 points) A clean Turing machine (cTM) is defined to be a Turing machine which satisfies the ad- ditional constraint that, at the end of each accepting computation, the tape is empty (i.e. all cells are blank) In this problem, you'll show that every Turing machine is equivalent to a clean Turing machine. To describe your construction, you'll first demonstrate how it works on an example, and then write out the general case formally a. Consider the Turing machine over the alphabet 2 0,1 given by the state diagram (using the usual conventions listed in Problem 1) 1:1,R 0:0,R 1:0,R q0 ac Draw the state diagram of a clean Turing machine that is equivalent to this one in JFLAP, export the image as a png or jpg file, and include it as part of your submission. You may use the standard conventions (like in Problem 1) for drawing state diagrams You do not need to justify your construction for credit, but if you describe how your state diagram works by explaining the role of each state and transition, we may be able to award partial credit if your answer is incorrect. b. Consider an arbitrary Turing machine M-Q. ? ?, ?,90,gacc ,grej). Define a clean Turing machine M' such that L(M) - L(M') by giving precise (but general) definitions for each parameter in the formal definition of M,-(2,,2, ?,, ,,96, qacc.4ej) For the purpose of your construction, you may assume that (D) to a non-blank cell of the tape. You do not need to justify your construction for credit, but if you describe how your construction works with an implementation-level description, we may be able to award partial credit if your answer is incorrect M does not ever write a blank symbol