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day9 - Factor Replacement Systems 3rd Model Click to edit...

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Click to edit Master subtitle style 10/4/11 Factor Replacement Systems 3rd Model Deceptively Simple
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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 22 Factor Replacement Concepts A factor replacement system (FRS) consists of a finite (ordered) sequence of fractions, and some starting natural number x. A fraction a/b is applicable to some natural number x, just in case x is divisible by b. We always chose the first applicable fraction (a/b), multiplying it times x to produce a new natural number x*a/b. The process is then applied to this new number. Termination occurs when no fraction is applicable. A factor replacement system partially computing n-ary function F typically starts with its argument encoded as powers of the first n odd primes.
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10/4/11 Dec 2, 2007/COT5310 © UCF (Charles E. Hughes) 33 Addition by FRS Addition is 3x15x2 becomes 2x1+x2 or, in more details, 203x15x2 becomes 2x1+x2 3050 2 / 3 2 / 5 Note that these systems are sometimes presented as rewriting rules of the form bx ° ax meaning that a number that has a factored as bx can have the factor b replaced by an a.
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