More wolf-slop.
The Wolfram S Combinator Challenge
11–20 of 24 posts
Re: The Wolfram S Combinator Challenge
#12S combinator always duplicates its last parameter, never deletes it. That's why K is needed for universality. This can be proved by induction. Or you can cite Craig's theorem (the less known one) for that. See [1] Honestly, I don't see the endgame here. [1] https://math.stackexchange.com/questions/839926/is-there-a-p...
cvoss, ezwoodland, tromp and v64 made a good point. As v64 points I was thinking of a Combinatory Completeness not Turing Completeness. Dropping that requirement as cvoss, ezwoodland, tromp point you can simulate deletion (that's what quantum computing does btw see No-deleting theorem).
I see the endgame now, thanks guys.
Re: The Wolfram S Combinator Challenge
#13Wait wouldn't this revolutionize computing? Seems like a rather low bounty for such a monumental proof
Re: The Wolfram S Combinator Challenge
#14Wait wouldn't this revolutionize computing? Seems like a rather low bounty for such a monumental proof
No? Why would it?
In the negative case, it would say the idea doesn't pan out.
In the positive case, it would mean that you can use just S instead of S and K when doing combinator reduction, but doesn't change that this kind of reduction is not super efficient practically speaking.
Re: The Wolfram S Combinator Challenge
#15Wait wouldn't this revolutionize computing? Seems like a rather low bounty for such a monumental proof
No? Why would it? In the negative case, it would say the idea doesn't pan out. In the positive case, it would mean that you can use just S instead of S and K when doing combinator reduction, but doesn't change that this kind of reduction is not super efficient practically speaking.
I was thinking in specifically the positive, would compression or encoding potentially allow for more compact representation of programs. Like Kolmogorovs
Re: The Wolfram S Combinator Challenge
#16> The S, K combinators defined by Moses Schönfinkel on December 7, 1920, are together known to be computation universal. On December 7, 2020, Stephen Wolfram made the suggestion that S alone might also be universal.
I wonder how long in advance Stephen Wolfram first had this thought and waited until the centennial to publicize the suggestion.
Re: The Wolfram S Combinator Challenge
#17Earlier quoted context omitted.
No? Why would it? In the negative case, it would say the idea doesn't pan out. In the positive case, it would mean that you can use just S instead of S and K when doing combinator reduction, but doesn't change that this kind of reduction is not super efficient practically speaking.
I was thinking in specifically the positive, would compression or encoding potentially allow for more compact representation of programs. Like Kolmogorovs
No not really. It's a thing you can do just because you can, like writing a book without the letter "e". Closer to the context of computation, it's like building a computer using only NAND gates. Or, given how restrictive the S combinator supposedly is, using only AND and OR gates. It won't make an efficient computer because your design is convoluted to all hell to make up for your choice to never use a NOT gate. Even the one made from NAND isn't efficient, because even though NAND can make any circuit without being too convoluted, it's not the most efficient way to make all circuits.
Re: The Wolfram S Combinator Challenge
#18The site doesn’t open from Ukraine. Any suggestion?
Re: The Wolfram S Combinator Challenge
#19Earlier quoted context omitted.
No? Why would it? In the negative case, it would say the idea doesn't pan out. In the positive case, it would mean that you can use just S instead of S and K when doing combinator reduction, but doesn't change that this kind of reduction is not super efficient practically speaking.
I was thinking in specifically the positive, would compression or encoding potentially allow for more compact representation of programs. Like Kolmogorovs
If anything, this would be a less compact representation.
Re: The Wolfram S Combinator Challenge
#20Needs a (2021)