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# hw6 - C is Turing-recognizable i± there is a decidable...

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CS 181 — Winter 2006 Problem Set #6 Formal Languages Due February 27, 2008 Problem 6.1. (10 points) Show that a language for which there exists an enumerator that enumer- ates the language in increasing lexicographical order is a decidable language. [For this, give a high level description of a Turing machine that halts on all inputs and accepts exactly the language.] Problem 6.2. (10 points) Show that a language
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Unformatted text preview: C is Turing-recognizable i± there is a decidable language D such that C = { x | ∃ y. ( h x,y i ∈ D ) } . Problem 6.3. (10 points) Show that {h G i | G is a CFG that generates inﬁnitely many strings } is decidable. Let C CFG = {h G,k i | L ( G ) contains exactly k strings where k ≥ 0 or k = ∞} . Show that C CFG is decidable. [Hint: Use the pumping length of G .]...
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