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# Introduction to the Theory of Computation

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Theory of Computation — CSE 105 Computability Study Guide Chapter 3: The Church–Turing Thesis 1. Exercises: 3, 6, 7, 8 — Page 147. 2. Problems: 9-15, 19, Page 149. Chapter 4: Decidability Problems: 10-22, Page 169–70. Chapter 5: Reducibility 1. Problems: 9-16, Page 195. 2. Suppose is recursively enumerable but not recursive. Show that for any Turing machine accepting , there must be infinitely many input strings for which loops forever. 3. Is the following statement true or false? If are recursively enu- merable subsets of , then is recursively enumerable. 4. Sketch a proof that if and are recursively enumerable subsets of , then both and are recursively enumerable. 5. Show that there exists a language so that neither nor (the comple- ment of ) is recursively enumerable. Can you give an example of such a

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