Question

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COMPSCI 110 37. Consider the following instruction set for a Turing machine (1,0,1,2,R) (1,1,1,1,R) (2,0, 1, 4, R) (2,1,1, 3, R) (3,0,1,5,R) (3,1,0,1,R) (4,0,0,2,R) (4,1,1,4,R) (5,0,1,2,R) (5,1,1,5, R) If the Turing machine is run on the tape 011001..., starting in statel on the first symbol on left of the tape, which state does it end up in after executing 6 instructions? A. State 5 B. State 2 C. State 4 D. State 3 E. State 1 38. Consider the following instruction set for a Turing machine (1,0,0,2,R) (1,1,0,4,R) (2,0,1,5, R) (2.1.0.3, R) (3,0,0,5, R) (3,1,0, 1, R) (4,0,0,2,R) (4,1,0,4,R) (5,0,1,2,R) (5,1,0, 4, R) If the Turing machine is run on the tape 111010.... starting in state 1 on the first symbol on the left of the tape, what is written on the tape after 6 instructions have been executed? A. ..000100... B. ...010000... C. ...001000... D. ...100000... E....000000...

Answer 1

Answer 37:

C. State 4

Explanation:

Instruction 1:
    Current state: 1
    Current tape content: ...011001...
    Currently pointing to symbol on tape: 0
    Executing instruction: (1, 0, 1, 2, R)
    Decoding above instruction: If machine is on state 1 and is pointing to tape symbol 0
                                then, write 1 on the current tape position (i.e., write 1
                                in place of 0), move to state 2 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...111001...
    State after the execution of above instruction: 2
    Now, pointing to tape symbol: 1
    
Instruction 2:
    Current state: 2
    Current tape content: ...111001...
    Currently pointing to symbol on tape: 1
    Executing instruction: (2, 1, 1, 3, R)
    Decoding above instruction: If machine is on state 2 and is pointing to tape symbol 1
                                then, write 1 on the current tape position (i.e., write 1
                                in place of 1), move to state 3 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...111001...
    State after the execution of above instruction: 3
    Now, pointing to tape symbol: 1
    
Instruction 3:
    Current state: 3
    Current tape content: ...111001...
    Currently pointing to symbol on tape: 1
    Executing instruction: (3, 1, 0, 1, R)
    Decoding above instruction: If machine is on state 3 and is pointing to tape symbol 1
                                then, write 0 on the current tape position (i.e., write 0
                                in place of 1), move to state 1 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...110001...
    State after the execution of above instruction: 1
    Now, pointing to tape symbol: 0
    
Instruction 4:
    Current state: 1
    Current tape content: ...110001...
    Currently pointing to symbol on tape: 0
    Executing instruction: (1, 0, 1, 2, R)
    Decoding above instruction: If machine is on state 1 and is pointing to tape symbol 0
                                then, write 1 on the current tape position (i.e., write 1
                                in place of 0), move to state 2 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...110101...
    State after the execution of above instruction: 2
    Now, pointing to tape symbol: 0
    
Instruction 5:
    Current state: 2
    Current tape content: ...110101...
    Currently pointing to symbol on tape: 0
    Executing instruction: (2, 0, 1, 4, R)
    Decoding above instruction: If machine is on state 2 and is pointing to tape symbol 0
                                then, write 1 on the current tape position (i.e., write 1
                                in place of 0), move to state 4 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...110111...
    State after the execution of above instruction: 4
    Now, pointing to tape symbol: 1
    
Instruction 6:
    Current state: 4
    Current tape content: ...110111...
    Currently pointing to symbol on tape: 1
    Executing instruction: (4, 1, 1, 4, R)
    Decoding above instruction: If machine is on state 4 and is pointing to tape symbol 1
                                then, write 1 on the current tape position (i.e., write 1
                                in place of 1), move to state 4 and move to next tape symbol
                                on the (R)ight.
    Tape content after the execution of above instruction: ...110111...
    State after the execution of above instruction: 4
    Now, pointing to tape symbol: Blank
    

Answer 38:

E. ...000000...

Explanation:

Similarly to question 37, the order of execution of instructions can be derived as follows:

	Instruction	Tape content after execution	State after execution
1	(1, 1, 0, 4, R)	...011010...	4
2	(4, 1, 0, 4, R)	...001010...	4
3	(4, 1, 0, 4, R)	...000010...	4
4	(4, 0, 0, 2. R)	...000010...	2
5	(2, 1, 0, 3, R)	...000000...	3
6	(3, 0, 0, 5, R)	...000000...	5

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