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aa:lab:03 [2020/10/21 12:27]
pdmatei 		aa:lab:03 [2020/10/23 14:43] (current)
pdmatei
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 ==== 1. Accepting and deciding a decision problem ==== ==== 1. Accepting and deciding a decision problem ====
  
-**1.1** Can the problem $math[f(w) = 0] (for all w in Sigma*) be accepted by a Turing Machine?+**1.1** Can the problem $math[f(w) = 0] (for all w in $math[\Sigma^*]) be accepted by a Turing Machine?
  
 **1.2** Can a problem be accepted by two different Turing Machines? **1.2** Can a problem be accepted by two different Turing Machines?
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 **1.3** Can a Turing Machine accept two different problems? **1.3** Can a Turing Machine accept two different problems?
  
-**1.4** Write a Turing Machine which accepts the problem $math[f(x) = 1] iff x (as binary) is odd, but does **NOT** decide it.+**1.4** Write a Turing Machine which accepts the problem $math[f(x) = 1] iff x (encoded ​as binary ​word) is odd, but does **NOT** decide it.
  
 **1.5** ​ Which of the following problems you think can be accepted and which can be decided? Use pseudocode instead of writing a TM. **1.5** ​ Which of the following problems you think can be accepted and which can be decided? Use pseudocode instead of writing a TM.
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 {{ :​aa:​lab:​wang_11_tiles.svg.png?​200 |}} {{ :​aa:​lab:​wang_11_tiles.svg.png?​200 |}}
   * Wang tiles can be used to tile surfaces, but each tile must be placed such that adjacent tiles have the **same color side**.   * Wang tiles can be used to tile surfaces, but each tile must be placed such that adjacent tiles have the **same color side**.
-  * The wang tiling decision problem is: //Is it possible to tile the plane (an infinite surface) with a given set of tiles?+  * The wang tiling decision problem is: //Is it possible to tile the plane (an infinite surface) with a given set of tiles//?
  
 **k-color** **k-color**
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 ==== 2. Complement ==== ==== 2. Complement ====
  
-**2.1** What is the complement of the previous ​problem?+**2.1** What is the complement of the problem ​from Exercise 1.1 ?
  
 **2.2** What is the complement of k Vertex Cover? **2.2** What is the complement of k Vertex Cover?
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 **2.3** If a problem is decided by some TM, can its complement be decided? **2.3** If a problem is decided by some TM, can its complement be decided?
  
-**2.4** If a problem is accepted by some TM, can its complement be decided?+**2.4** If a problem is accepted by some TM, can its complement be accepted?
  
 ==== 3. Turing Machine pseudocode ==== ==== 3. Turing Machine pseudocode ====
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 Suppose M is encoded on binary words, and also working on binary words, for simplicity. Suppose M is encoded on binary words, and also working on binary words, for simplicity.
  
 +/* Solution:
 <​code>​ <​code>​
 Pseudocode(M):​ <- input Pseudocode(M):​ <- input
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         repeat the same process all over         repeat the same process all over
 </​code>​ </​code>​
 +
 +*/
  
 **3.2** Which of the following pseudocode is a proper Turing Machine? Explain why. **3.2** Which of the following pseudocode is a proper Turing Machine? Explain why.