Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Tetration and higher-order operations on transfinite ordinals
#8
bo198214 Wrote:[...]
Just skimmed through your article and asking myself how this function can be expressed with a recursive definition ...
I've not thought about that... but I assume it must be possible since the algorithm obviously can be expressed as a Turing machine, so it must be recursive. I'm not sure how exactly to go about deriving a recursive definition for it, though.

Maybe one way is to perform a depth-first traversal on the tree, left child first, and recursively linearize the left-most children. So, in computer pseudocode, it could be something like this:

Code:
linearize(T,m) {
    if (is_rightbranching_chain(T.left_subtree) and
        is_rightbranching_chain(T.right_subtree))
    {
        ... (perform the transformation... not sure how to express this recursively yet)
    } else {
        T.left_subtree = linearize(T.left_subtree, m);
        T.right_subtree = linearize(T.right_subtree, m);
        return T;
    }
}

Once we work out the pseudocode, maybe there's a way to factor it into a recursive function...?
Reply


Messages In This Thread
RE: Tetration and higher-order operations on transfinite ordinals - by quickfur - 03/29/2008, 04:01 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 258 09/09/2019, 10:38 PM
Last Post: tommy1729
  Could there be an "arctic geometry" by raising the rank of all operations? Syzithryx 2 415 07/24/2019, 05:59 PM
Last Post: Syzithryx
  Intresting ternary operations ? tommy1729 0 1,511 06/11/2015, 08:18 AM
Last Post: tommy1729
  on constructing hyper operations for bases > eta JmsNxn 1 2,502 04/08/2015, 09:18 PM
Last Post: marraco
  Means and intermediate operations (was: Rational operators (a {t} b); a,b > e solved) Cherrina_Pixie 3 5,132 06/14/2011, 09:52 PM
Last Post: JmsNxn
  Ackermann function and hyper operations andydude 3 6,512 04/18/2011, 05:08 PM
Last Post: bo198214
  Operations with fractional index between + and * ? Gottfried 6 8,514 10/21/2009, 01:30 AM
Last Post: andydude
  Poll: hyper-operations terminology Base-Acid Tetration 3 5,158 08/22/2009, 05:08 PM
Last Post: Base-Acid Tetration
  interesting pattern in hyper-operations Base-Acid Tetration 8 10,734 05/04/2009, 09:15 PM
Last Post: BenStandeven
  Hilberdink: Uniqueness by order of growth? bo198214 2 3,556 05/30/2008, 12:29 AM
Last Post: andydude



Users browsing this thread: 1 Guest(s)