Module 11 Worksheet - Computability and Languages | CSE 460, Study notes of Computer Science

Material Type: Notes; Professor: Torng; Class: Computability and Languages; Subject: Computer Science & Engineering; University: Michigan State University; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 07/23/2009

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Module 11 Worksheet
In Class Questions
1) (S9) The variable x is an input to what problem and thus consists of what?
2) (S9) The variable PT(x) is an input to what problem and thus consists of what?
3) (S11) What would happen if PT infinite looped on some legal input Q,y?
4) (S11) Is it possible that PL infinite loops on some input PT(x)? Why or why not?
5) (S24) Is the following a yes or no input instance for problem L? Why or why not?
Assume = {a}.a}.
bool main(string z) {a}.
if (z = = aa) return (yes);
else return(no);
}
6) (S27) What is Y(Q1)?
7) (S27) Is Q1 a yes or no input to L?
8) (S27) What does PL output when given Q1 as input?
9) (S27) What is Y(Q2)?
10) (S27) Is Q2 a yes or no input to L?
11) (S27) What does PL output when given Q2 as input?
12) (S28) What is Y(QL)?
13) (S28) Is QL a yes or no input to L?
14) (S28) What does PL output when given QL as input?
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Module 11 Worksheet In Class Questions

  1. (S9) The variable x is an input to what problem and thus consists of what?
  2. (S9) The variable PT(x) is an input to what problem and thus consists of what?
  3. (S11) What would happen if PT infinite looped on some legal input Q,y?
  4. (S11) Is it possible that PL infinite loops on some input PT(x)? Why or why not?
  5. (S24) Is the following a yes or no input instance for problem L? Why or why not? Assume  = {a}.a}. bool main(string z) {a}. if (z = = aa) return (yes); else return(no); }
  6. (S27) What is Y(Q 1 )?
  7. (S27) Is Q 1 a yes or no input to L?
  8. (S27) What does PL output when given Q 1 as input?
  9. (S27) What is Y(Q 2 )?
  10. (S27) Is Q 2 a yes or no input to L?
  11. (S27) What does PL output when given Q 2 as input?
  12. (S28) What is Y(QL)?
  13. (S28) Is QL a yes or no input to L?
  14. (S28) What does PL output when given QL as input?

For the following two questions, imagine we replace 5 and make it an unsigned int variable y.

  1. (S28) What is Y(QL) in terms of y?
  2. (S28) As a function of y, what does PL output when given QL as input?
  3. (S29) What is Y(QL) in terms of QH and y?
  4. (S29) As a function of QH and y, what does PL output when given QL as input? For the following two questions, imagine we make QYL into a program variable.
  5. (S29) What is Y(QL) as a function of QH, y, and QYL.
  6. (S29) As a function of QH, QYL, and y, what does PL output when given QL as input?
  7. (S30) Is QH,y a yes or no input instance to the Halting Problem in this case?
  8. (S30) What will QL do on input aaa?
  9. (S30) What will PL do on input QL?
  10. (S30) Suppose we changed the 5 to a 3. How would the listing of QL change?