Hw10 - Homework 10 CISC 303 Timo Kötzing([email protected]

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Unformatted text preview: Homework 10 CISC 303 Timo Kötzing ([email protected]) Handed out: Monday, May 4. Due Date: Friday, May 8. Problem 1. (2 or 8 points) Let f : N 2 → N , ( x,y ) 7→ x + y ( f is addition on natural numbers). If you have showed that f is computable when all inputs are unary, show that f is also computable when the inputs are binary (8pts). If you have showed that f is computable when all inputs are binary, show that f is also computable when the inputs are unary (2pts). Problem 2. (8 points) Use the characterization given in Theorem 3.2.1 of the Lecture Notes to show that the following two functions are (total) computable. (i) g : N 2 → N , ( x,y ) 7→ x · y ; (ii) g 1 : N → N ,x 7→ x ! . 1 Problem 3. (8 points) (i) Prove informally that L = { code( M ) | M TM and M halts on ε in ≤ 1000 steps } is decidable. (ii) Prove informally that L = { code( G ) | G is ambiguous CFG } , the Ambiguity Problem for CFGs , is semi- decidable....
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