The Answers for Homework

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The Answers for Homework 11

• 1-1. The TM is similar to the copier in example
  2. The only difference is in step 3 instead of
  create a 1, we create 11.
• 1-2. The TM contains 3 stages
• Stage 1 copy x to its left-side (x ? 2x)
• Stage 2 use the TM in 1-1 for y (y ?3y)
• Stage 3 use the adder TM.

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The Answers for Homework 11

• 1-3. The TM program can be divided into the
  following 3 parts
• Part I find the rightmost 1s (up to 5 1s)

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The Answers for Homework 11

• Part II if there are 5 1s then remove them.

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The Answers for Homework 11

• Part III Halting process (go to final state q12
  if there are less than 5 1s left).

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The Answers for Homework 11

• 2-1. Assume the initial and final tape contents
  are 010n and , respectively.
• The TM can be seen as a repeated copier of the
  current content between the two 0s for each 1 in
  n (0m0 ? 02m0). The pseudo-code of the TM
  program is shown below

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The Answers for Homework 11

• Step 1 repeat the following until n contains no
  more 1s
• - find a 1 in n and replace it with symbol a
• - copy m in 0m0 (0m0 ? 02m0)
• Step 2 replace all as with 1s

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The Answers for Homework 11

• 2-2. Assume the initial and final tape contents
  are 010n and 0n!0n, respectively.
• The TM can be seen as a repeated multiplier of
  the current content between the two 0s with the
  current number following the 2nd 0 (0x0yaa ?
  0xy0yaa). The pseudo-code of the TM program is
  shown below

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The Answers for Homework 11

• Step 1 replace all 1s in n by as
• Step 2 repeat the following until n contains no
  more as
• - replace the leftmost a by 1
• - replace x in 0x0 by xy (0x0yaa ? 0xy0yaa).