Talk:Sudan function

Please check wether the definition is good. My source isn't a very reliable one (random google search, namely ). I hope it's ok, however--it looks enough similarly to the Ackermann function to me to think it grows fast, as it should.

Is the table of values right?
I have an assignment for entry level Computer Science which is to implement the Sudan function recursively. I was trying to find some sample values to see if I had implemented it correctly, so I came to the wikipedia article. My program was not working- or so I thought. The table in the article is correct if you change the third condition's second argument to F(x, y) + y-leaving out the plus 1. Can anyone more skilled speak to this?

137.54.8.99 (talk) 21:38, 15 March 2010 (UTC)

Follow up- I read it wrong. Article is right.

137.54.8.99 (talk) 21:43, 15 March 2010 (UTC)

What is exactly the Sudan function ?
The article does not say what the Sudan function exactly is, as it defines a sequence $$(F_n)_{n\ge0}$$ of functions.

Perhaps it should be more appropriate to write the function $$F(n,x,y)$$ whith three arguments. Pierre de Lyon 11:49, 19 May 2006 (UTC)


 * Would that make the definition:
 * $$F(0, x, y) = x+y,\,$$
 * $$F(n+1, x, 0) = x, \ n \ge 0\,$$
 * $$F(n+1, x, y+1) = F(n, F(n+1, x, y), F(n+1, x, y) + y + 1), \ n\ge 0.\,$$
 * or shortened:
 * $$F(0, x, y) = x+y,\,$$
 * $$F(n, x, 0) = x, \ n \ge 1\,$$
 * $$F(n, x, y) = F(n-1, F(n, x, y-1), F(n, x, y-1) + y), \ n\ge 1.\,$$
 * ? -  &#x211A;  uackor 20:02, 25 September 2007 (UTC)


 * This is exactly what I meant. By the way, I prefer the first definition which refers more to its inductive definition and makes a difference between the cases  $$0$$ and $$n+1$$. Pierre de Lyon 17:37, 30 October 2007 (UTC)

The function here doesn't match Sudan's paper
I checked both the 1979 article and the 1927 paper, and both of them describe Sudan's function as a function that uses transfinite recursion as follows:


 * $$\psi(a,b,0) = a+b$$
 * $$\psi(a,b,n+1) = t_c(a,\lambda_m \psi(c,m,n),b)$$

where
 * $$t_c(a,f(c),0) = a$$
 * $$t_c(a,f(c),n+1) = f(t_c(a,f(c),n+1))$$.

I don't understand the functions in the paper well enough at the moment to interpret them. The source linked above attributes the function as given to MR 82k:03061 but I can't interpret this identifier. Arcorann (talk) 09:30, 1 May 2020 (UTC)