<p>I am new to the site and I hope after reading the guide lines i am in line with them.
I am reading The Art of Computer Programming by Donald E. Knuth. The question is addressed to those having a copy of Volume 1. At pages 27-28, Knuth formally defines a <em>computational method</em> to be a quadruple (Q, I, $\omega$, f). I am interested in the first <em>computational method</em>. </p>

<p>1/ Then he goes on defining Q as being <em>states of the computation</em>. What exactly are states of computations?</p>

<p>2/ The Euclid algorithm on page 22 is formalized in the defined <em>computational method</em>, but if Q is made up of (m,n), (n), (m,n,r,1), (m,n,r,2) and (m,n,p,3) are those the states of computation and how do you come up with them? and how does one recognize them from an algorithm. more precisely, how do you translate a given algorithm into the given computational method?</p>

<p>3/ How are the values of <em>f</em> deduced from the algorithm?</p>

<p>P.S. In case my question is vague please mention in comments where i need to make things clear.
And I am more after understanding the theory than any algorithm usefulness, hope that will be useful.</p>

CC BY-SA 3.0
2011-11-16T12:33:10.447Z
I don't think the question is vague, but I also think it is not as research-levelly as we typically expect. So maybe this is a great question for math.SE?
Raphael
CC BY-SA 3.0
2011-11-17T22:54:30.303Z
@Raphael: I thought about math.SE but I realize rare are mathematicians with a copy of TAOCP. I'm still trying to understand it clearly and when I do, I'll post the answer. Thanks
Toussaint
CC BY-SA 3.0
2011-11-18T10:51:56.040Z
The thing is, a couple of computer scientists roam math.SE, too, and will definitely answer the question if asked there (if they can, that is).
Raphael
CC BY-SA 3.0
2014-02-11T17:44:44.770Z
There's also cs.SE!
Joshua Grochow
<ds.algorithms>
D. Knuth definition of a computational method
Toussaint
# D. Knuth definition of a computational method

(Asked by: username_0 on 2011-11-15)

I am new to the site and I hope after reading the guide lines i am in line with them.
I am reading The Art of Computer Programming by Donald E. Knuth. The question is addressed to those having a copy of Volume 1. At pages 27-28, Knuth formally defines a *computational method* to be a quadruple (Q, I, $\omega$, f). I am interested in the first *computational method*.

1/ Then he goes on defining Q as being *states of the computation*. What exactly are states of computations?

2/ The Euclid algorithm on page 22 is formalized in the defined *computational method*, but if Q is made up of (m,n), (n), (m,n,r,1), (m,n,r,2) and (m,n,p,3) are those the states of computation and how do you come up with them? and how does one recognize them from an algorithm. more precisely, how do you translate a given algorithm into the given computational method?

3/ How are the values of *f* deduced from the algorithm?

P.S. In case my question is vague please mention in comments where i need to make things clear.
And I am more after understanding the theory than any algorithm usefulness, hope that will be useful.

**Tags:** ds.algorithms

> **Comments:**
> **username_1**: I don't think the question is vague, but I also think it is not as research-levelly as we typically expect. So maybe this is a great question for math.SE?  
> **username_0**: @username_1: I thought about math.SE but I realize rare are mathematicians with a copy of TAOCP. I'm still trying to understand it clearly and when I do, I'll post the answer. Thanks  
> **username_1**: The thing is, a couple of computer scientists roam math.SE, too, and will definitely answer the question if asked there (if they can, that is).  
> **username_2**: There's also cs.SE!  

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## 0 answers

