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hw7 - A TM Show that J is neither recognizable nor...

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CS 181 — Winter 2006 Problem Set #7 Formal Languages Due March 5, 2008 Problem 7.1. (10 points) A useless state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any useless states. Formulate this problem as a language and show that it is undecidable. Problem 7.2. (10 points) Let J = { w | either w = 0 x for some x A TM or w = 1 y for some y
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Unformatted text preview: A TM } . Show that J is neither recognizable nor co-recognizable. Problem 7.3. (10 points) Show that A is decidable i± A ≤ m * 1 * . Show that ≤ m is reﬂexive and transitive. Show that there is an undecidable subset of 1 * . [Hint: Take any undecidable set in { , 1 } * , and think about each element in the set as a binary number. Encode the number in unary.]...
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