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Introduction to the Theory of Computation

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Unformatted text preview: Theory of Computation -- CSE 105 Computability Study Guide Chapter 3: The ChurchTuring Thesis 1. Exercises: 3, 6, 7, 8 -- Page 147. 2. Problems: 9-15, 19, Page 149. Chapter 4: Decidability Problems: 10-22, Page 16970. 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 enumerable subsets of , then is recursively enumerable. 5. Show that there exists a language so that neither nor (the complement of ) is recursively enumerable. Can you give an example of such a language? 1 (a) Given a Turing machine and a nonhalting state , does state , starting with an empty tape? ever enter 6. Show that the following problems are unsolvable. For a Turing machine denotes the language accepted by . 4. Sketch a proof that if and are recursively enumerable subsets of then both and are recursively enumerable. ) "! $# ) , , ' % ( & (b) Given a Turing machine , does it accept more than one string? (c) Given two Turing machines and , is (d) Given a Turing machine , is the language (e) Given a Turing machine , is the language it accepts the complement of a recursively enumerable language? 2 A FE 8. Show that the language accepts is not recursive. A &@ 7. Show that the language recursively enumerable. halts on input ' 0 $' 0 % 1 % 98 64 3 2 ( 75 98 64 3 2 D 7CB ? accepts regular? is not recursive but ...
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This test prep was uploaded on 02/08/2008 for the course CSE 105 taught by Professor Paturi during the Summer '99 term at UCSD.

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