ass1_1_2006

ass1_1_2006 - MATH 335 001 Computational Algebra Winter...

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Unformatted text preview: MATH 335 001 Computational Algebra Winter 2006 Assignment 1. Part 1. 1) Define by recursion the function x → xm , x, m ∈ N and specify precisely the functions f and g from the corresponding recursion scheme. 2) Show that the function ˙ x−y = x − y, 0, if x ≥ y, otherwise ; is computable by a RAM machine. 3) Show that the function f (x) = undef ined, 1 3 x, if x is a multiple of 3, otherwise; is computable by some RAM machine. 4) Write down a program for a Turing machine that computes the following function x → 2x, x ∈ N. 5) Write down a program for a Turing machine that computes the following function 0, if x = 3k for some k , 1, if x = 3k + 1 for some k , rest3 (x) = 2, if x = 3k + 2 for some k , where x ∈ N. ...
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This note was uploaded on 02/20/2011 for the course MATH 335 taught by Professor Miasnykov during the Fall '06 term at McGill.

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