{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–4. Sign up to view the full content.

Click to edit Master subtitle style 10/4/11 Factor Replacement Systems 3rd Model Deceptively Simple

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern