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Unformatted text preview: Maintain one prime per RM instruction Instruction 1,2,,m p n+1 ,p n+2 ,,p n+m Keep one last prime to represent halt state p n+m+1 Simulating Behavior of RM For each instruction 1 j m If j is an INC instruction (j. INC k [ l ]) Add FRS rule p n+j x p n+ l p k x If j is a DEC instruction (j. DEC k [p,z]) Add FRS rule p n+j p k x p n+p x Add FRS rule p n+j x p n+z x Cleanup rules 0 i n1 p n+m+1 p i x p n+m+1 x Finally p n+m+1 x x Example Limited Subtraction Register Machine r2 r1 r2, if r1 r2; 0, otherwise Factor Replacement System Input: 3 x 5 y Output: 2 z where z = x y, if x y; 0, otherwise Example Limited Subtraction 1. DEC2[2,3] 2. INC1[1] 3. DEC3[4,5] 4. DEC1[3,3] 5. 3*7x 11x 7x 13x 11x 2*7x 5*13x 17x 13x 19x 2*17x 13x 17x 13x Associated Primes 7 11 13 17 19...
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 Fall '10
 Dutton

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