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midterm - CSC544 Spring 2011 Midterm Take-Home Exam due in...

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CSC544 Spring 2011 Midterm Take-Home Exam due in class Tuesday 3/29/11 Note: All work has to be your own, no team work allowed. Part A, short answers, 40 points. 1. (5 points) Why do we think of decidable language as representing algorithms? 2. (5 points) What do we mean when we say that two machines are equivalent? 3. (5 points) In your own words; describe the halting problem . 4. (5 points) In your own words describe the Church-Turing thesis. 5. (5 points) Compute the normal form of the following λ -expression, ( λx. λy. x y ) ( λx. x + 1) 3 6. (5 points) Show that the language L = { w | w has an even number of 0s, or 1s, or both } is a regular language. 7. (5 points) What do we mean when we say that the language L is not Turing-recognizable ? 8. (5 points) What does M accepts the string w mean when M is a nondeterministic automaton or Turing machine? 1
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Part B, problems, 60 points. 1. (10 points) Given the language L = { ww R | w ∈ { a, b } } where w R is the reverse of the string w , do the following, 1. Show that the language L is not regular.
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