{ "translations": { "en": { "q1": { "type": "select", "description": "Let's first guess what the following turing machine does.
Suppose w represents the input string and the current tape is #w#, answer the question on the right.", "question": "Select one of the following statements that best describe this turing machine.", "answer": [ "A copy machine that transforms #w# into #w#w#." ], "choices": [ "A shift machine that can shift a string to the LEFT of its original tape.", "A copy machine that transforms #w# into #ww#.", "A copy machine that transforms #w# into #w#w#.", "A copy machine that transforms #w# into ww." ] }, "q3": { "type": "select", "description": "Before we start, let's take a look at the below turing machine and answer the question on the right.", "question": "Which machine is the initial machine of this copy machine.", "answer": [ "$>L_{\\#}$" ], "choices": [ "$R$", "$>L_{\\#}$", "$R\\#$", "$L^{2}_{\\#}$" ] }, "q4": { "type": "select", "description": "You are correct! Do you know what the $>L_{\\#}$ machine does?", "question": "What does the $>L_{\\#}$ machine do?", "answer": [ "$>L_{\\#}$ means going to the closest empty cell on the left, from the head." ], "choices": [ "$>L_{\\#}$ means going to one cell on the left, and then change the cell to #.", "$>L_{\\#}$ means going back to the previous machine of the turing machine.", "$>L_{\\#}$ means going to the closest empty cell on the left, from the head." ] }, "q5": { "type": "true/false", "description": "Your classmate Alan says that the initial machine $>L_{\\#}$ means we need to go to the closest space (denoted by #) on the left, from the head.", "question": "Is that a true statement?", "answer": [ "True" ], "choices": [ ] }, "q6": { "type": "select", "description": "Excellent! We start from the $>L_{\\#}$. $L_{\\#}$ means going to the closest space (denoted by #) on the left, from the head. ", "question": "We will then move to the next machine $R$ by following the arrow direction.
What does the next machine $R$ mean?", "answer": [ "$R$ means moving from the current tape cell to the right tape cell." ], "choices": [ "$R$ means moving from the current tape cell to the right tape cell.", "$R$ means moving from the current tape cell to the next # cell on the right." ] }, "q7": { "type": "select", "description": "Well Done! $R$ means moving from the current tape cell to the right tape cell.
Now we can see that $R$ is followed by two arrows pointing to either right or down.
Answer the questions on the right to determine which arrow direction you should follow.", "question": "Is the current tape cell a space or empty(i.e. #)? Then, which arrow direction should you follow? (Select all the correct answers.)", "answer": [ "No, it is not a space($\\overline{\\#}$).", "Follow the arrow pointing right." ], "choices": [ "Yes, it is a space(#).", "No, it is not a space($\\overline{\\#}$).", "Follow the arrow pointing right.", "Follow the arrow pointing down." ] }, "q8": { "type": "select", "description": "[Explanation to the questions on the previous slide.]
Is the current tape cell a space (i.e. #)?
No, the current tape cell is an 'a', so we follow the $\\overline{\\#}$ direction to go to the # machine.", "question": "Now, we are at the # machine.
What will the # machine do to the tape?", "answer": [ "erase the highlighted 'a' by making the tape cell empty (denoted by #)." ], "choices": [ "erase the highlighted 'a' by making the tape cell empty (denoted by #).", "change the current position to the next empty cell (denoted by #) on the RIGHT.", "change the current position to the next empty cell (denoted by #) on the LEFT." ] }, "q9": { "type": "select", "description": "Well Done! The # machine just replaced 'a' with '#'.
We are now at the $R^{2}_{\\#}$ machine.", "question": "What will the $R^{2}_{\\#}$ machine do to the tape?", "answer": [ "$R^{2}_{\\#}$: change the current position to the second space(#) on the right." ], "choices": [ "$R^{2}_{\\#}$: change the current position to the second space(#) on the right.", "$R^{2}_{\\#}$: change the current position to the second cell on the right and then write '#' to the tape cell.", "$R^{2}_{\\#}$: change the current position to the next cell on the right and then write two '#' to the cell." ] }, "q10": { "type": "select", "description": "Now we are at the Sigma($\\sigma$) machine.
Your classmate Nikola says that $\\sigma$ means writing the letter we just read to the current tape cell.", "question": "Is Nikola's statement correct? If yes, what value should the machine write to the current tape cell?", "answer": [ "a", "Yes, Nikola's statement is correct." ], "choices": [ "a", "b", "#", "Yes, Nikola's statement is correct.", "No, Nikola's statement is incorrect." ] }, "q11": { "type": "select", "description": "Awesome! The machine just wrote 'a' to the cell.
Now, $L^{2}_{\\#}$ looks very similar to $R^{2}_{\\#}$. $L^{2}_{\\#}$ means changing the current tape position to the second space(#) on the LEFT.
Notice how the $L^{2}_{\\#}$ machine unhighlighted the previous positions and then highlighted the current position.", "question": "We will enter the next Sigma($\\sigma$) machine. What value will the next $\\sigma$ machine write to the current tape cell?", "answer": [ "a" ], "choices": [ "a", "b", "#" ] }, "q12": { "type": "select", "description": "Excellent! Sigma($\\sigma$): Write the letter we just read to the current tape cell.
We just read 'a', so we needed to write 'a' to the cell.", "question": "We will go back to the $R$ machine following the attached arrow.
(Fill in the blank) Suppose that the currently highlighted cell is at position 1, the $R$ machine will change the highlighted position to position _", "answer": [ "2" ], "choices": [ "1", "0", "2", "3", "4" ] }, "q13": { "type": "select", "description": "Awesome! $R$ just changed the highlighted position from 1 to 2.
Now we can see that $R$ is followed by two arrows pointing to either right or down.
Answer the questions on the right to determine which arrow direction you should follow.", "question": "Is the current tape cell a space or empty(i.e. #)? Then, which arrow direction should you follow? (Select all the correct answers.)", "answer": [ "No, it is not a space($\\overline{\\#}$).", "Follow the arrow pointing right." ], "choices": [ "Yes, it is a space(#).", "No, it is not a space($\\overline{\\#}$).", "Follow the arrow pointing right.", "Follow the arrow pointing down." ] }, "q14": { "type": "select", "description": "[Explanation to the questions on the previous slide.]
Is the current tape cell a space (i.e. #)?
No, the current tape cell is an 'b', so we follow the $\\overline{\\#}$ direction to go to the # machine.", "question": "Now, we are at the # machine.
What will the # machine do to the tape?", "answer": [ "erase the highlighted 'b' by making the tape cell empty (denoted by #)." ], "choices": [ "erase the highlighted 'b' by making the tape cell empty (denoted by #).", "change the current position to the next empty cell (denoted by #) on the RIGHT.", "change the current position to the next empty cell (denoted by #) on the LEFT." ] }, "q15": { "type": "select", "description": "Well Done! The # machine just replaced 'b' with '#'.
We are now at the $R^{2}_{\\#}$ machine.", "question": "Suppose the highlighted cell is currently at position 2, after performing the $R^{2}_{\\#}$ machine, at which position will the next highlighted cell be?", "answer": [ "5" ], "choices": [ "4", "5", "6", "7", "3" ] }, "q16": { "type": "select", "description": "Now we are at the Sigma($\\sigma$) machine. $\\sigma$ means writing the letter we just read to the current tape cell.", "question": "What value should you write to the current tape cell?", "answer": [ "b" ], "choices": [ "a", "b", "#" ] }, "q17": { "type": "select", "description": "$L^{2}_{\\#}$: Go to the second space(#) on the left.", "question": "Suppose the currently highlighted cell is at position 5, the next highlighted cell will be at position _", "answer": [ "2" ], "choices": [ "2", "3", "4", "1" ] }, "q18": { "type": "select", "description": "Now we are at the Sigma($\\sigma$) machine. $\\sigma$ means writing the letter we just read to the current tape cell.", "question": "What value should you write to the current tape cell?", "answer": [ "b" ], "choices": [ "a", "b", "#" ] }, "q19": { "type": "select", "description": "Excellent! Sigma($\\sigma$): Write the letter we just read to the current tape cell.
We just read 'b', so we needed to write 'b' to the cell.", "question": "We go back to the $R$ machine following the attached arrow.
(Fill in the blank) Suppose that the currently highlighted cell is at position 2, the $R$ machine will change the highlighted position to position _", "answer": [ "3" ], "choices": [ "3", "4", "5", "2" ] }, "q20": { "type": "select", "description": "$R$ is followed by two different arrows. Answer the questions to determine which arrow direction you should follow.", "question": "Is the current tape cell a space or empty(i.e. #)? Then, which arrow direction should you follow? (Select all the correct answers.)", "answer": [ "Yes, it is a space(#).", "Follow the arrow pointing down." ], "choices": [ "Yes, it is a space(#).", "No, it is not a space($\\overline{\\#}$).", "Follow the arrow pointing right.", "Follow the arrow pointing down." ] }, "q21": { "type": "select", "description": "Is the current tape cell a space (i.e. #)?
Yes, the current tape cell is #, so we follow the # direction to go to the $R\\#$ machine.
", "question": "Now, what does the $R_{\\#}$ mean?", "answer": [ "$R_{\\#}$ means going to the closest empty cell on the right." ], "choices": [ "$R_{\\#}$ means going to one cell on the right, and then change the cell to #.", "$R_{\\#}$ means going back to the previous machine of the turing machine.", "$R_{\\#}$ means going to the closest empty cell on the right." ] } } } }