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# day16 - Equivalence of Models Click to edit Master subtitle...

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Click to edit Master subtitle style 10/4/11 Equivalence of Models Equivalency of computation by S - programs, register machines, factor replacement systems, recursive functions and Turing machines

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Click to edit Master subtitle style 10/4/11 S-Machine l REGISTER
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 33 S Program ≤ Reg. Machine Let P be an S Program consisting of m instructions computing f(x1,…, xn). Assume the highest indexed temporary variable is Z t Define the mapping g, g(X i ) = i, 1…iw n, g(Y) = n+1, and g(Z j ) = n+j+1, 1 °jt t. Change each IF V p0 GOTO L to IF V™ 0 GOTO A k , where L is the k-th instruction, or if L is E, k=m+1 Map the j-th S instruction by [A j ] V V maps to 2j-1. DEC n+t+2 (2j,2j) 2j. DEC n+t+2 (2j+1,2j+1) [A j ] V V+1 maps to 2j-1. INC g(v) (2j) 2j. DEC n+t+2 (2j+1,2j+1) [A j ] V V-1 maps to

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 44 Reg. Machine ≤ S Program Let M be a Register Machine consisting of m instructions computing f(x1,…, xn). Assume highest indexed register is R s Define the mapping g, g(i)=X i , 1± i±n, g(n+1)=Y, and g(i)=Z i-n-1 , n+2±i± s.
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day16 - Equivalence of Models Click to edit Master subtitle...

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