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# Hw9 - Homework 9  CISC 303 Timo Kötzing([email protected]

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Unformatted text preview: Homework 9  CISC 303 Timo Kötzing ([email protected]) Monday, April 27. Friday, May 1. Handed out: Due Date: (8 points) Let f : N2 → N, (x, y ) → x + y (f is addition on natural numbers). Show that f is computable by explicitly giving a TM computing f . Problem 1. Problem 2. (8 points) (i) Argue informally (using the Church-Turing Thesis) that K = {code(M)|w | M TM and w ∈ L(M)} is semidecidable (K is the set of all codes of TMs, followed by a |-symbol, followed by a word accepted by that TM). (ii) Argue informally (using the Church-Turing Thesis) that L = {code(M) | M TM and L(M) = ∅} is semidecidable. Problem 3. (8 points) (i) Prove formally (ii) Prove formally languages, is that L = {code(M) | M TM and ε ∈ L(M)}, the ε-Halting that L = {code(M) | M TM and L(M) = ∅}, the decidable. not 1 Problem, is not decidable. Emptyness Problem for semi-decidable ...
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