Unformatted text preview: m,n computes the remainder of m after division by n . Write down a program for a RAM over N 2 that for given numbers m,n ∈ N computes their greatest common divisor gcd ( m,n ). [ Hint : Use the Euclidean algorithm] b) Estimate the time complexity of the algorithm in a). 4) Let γ : M → γ ( M ) ∈ N be the enumeration of Turing machine programs M discussed in the class. Find the program M such that γ ( M ) = 24. 5) a) Enumerate eﬀectively all programs for Random Access Machines (RAM). b) Explain how one can try to write down a program for universal RAM for one variable functions....
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 Fall '06
 Miasnykov
 Algebra, Addition, Remainder, Natural Numbers, Natural number, random access, Euclidean algorithm, common divisor gcd

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