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Computer Science 172 - Fall 1995 - Sinclair - Midterm 2

Computer Science 172 - Fall 1995 - Sinclair - Midterm 2 -...

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CS172Fall95Quiz2.html Quiz 2 Instructions: Please write your name at the top of this sheet. There are two questions on this quiz. Please answer each question on its own sheet of paper, using the back of the sheet to continue your answer. You may assume without proof any result that was proven in class or on a homework, provided you state it clearly. Please write clear, concise answers. If you are having problems with a part of a question, leave it and try the next one. The two questions carry approximately equal credit. 1. Consider the following problem: INSTANCE: A binary Turing machine M. QUESTION: Does M accept at least 10 strings> The above problem can be formulated as the problem of recognizing the language L >=10 = { <M> : M accepts at least 10 strings }. (Hear <M> denotes the standard encoding of a binary TM.) (a) Show that the language L >=10 is recursively enumerable (r.e.). (b) Recall that the language L halt , defined by L halt = { <M>\$x : M halts on x } is not recursive. By giveng a reduction from L halt to L >=10 , prove that is L >=10 not recursive.

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Computer Science 172 - Fall 1995 - Sinclair - Midterm 2 -...

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