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# day19 - RSIVEACTOR F Click to edit Master subtitle style...

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Click to edit Master subtitle style 10/4/11 FACTOR ° URSIVE

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 22 Universal Machine In the process of doing this reduction, we will build a Universal Machine. This is a single recursive function with two arguments. The first specifies the factor system (encoded) and the second the argument to this factor system. The Universal Machine will then simulate the given machine on the selected input.
10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 33 Encoding FRS Let (n, ((a1,b1), (a2,b2), … ,(an,bn)) be some factor replacement system, where (ai,bi) means that the i-th rule is aix l bix Encode this machine by the number F, p p p p n n n n n b a b a b a n n 2 2 1 2 2 1 2 11 7 5 3 2 2 2 1 1 + + -

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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 44 Simulation by Recursive # 1 We can determine the rule of F that applies to x by RULE(F, x) = H z (1 ≤ z ≤ exp(F, 0)+1) [ exp(F, 2*z-1) | x ] Note: if x is divisible by ai, and i is the least integer for
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