Anonymous at Fri, 8 Nov 2024 22:29:19 UTC No. 16467644

>>16467628
https://en.wikipedia.org/wiki/IMPLY_gate
https://en.wikipedia.org/wiki/NIMPLY_gate
https://quantumcomputing.stackexchange.com/questions/39822/boosting-amplitude-of-imply-gate

Anonymous at Fri, 8 Nov 2024 22:45:24 UTC No. 16467654

>>16467628
>was commutative algebra
What does this have to do with commutative algebra?

Anonymous at Fri, 8 Nov 2024 22:57:23 UTC No. 16467668

>>16467654
the IMPLY gate is non-commutative.

and in Stanley Williams labs, they got a computation speedup implementing universal logic with NIMPLY instead of NAND or NOR

nature likes the path or least resistance,

Anonymous at Fri, 8 Nov 2024 23:02:28 UTC No. 16467671

>>16467668
That has jackshit to do with commutative algebra. Don't use terms you don't understand because you're embarrassing yourself.
All you're saying is that p=>q is not equivalent to q=>p which is obvious.

Anonymous at Fri, 8 Nov 2024 23:18:26 UTC No. 16467693

>>16467671
this is important in the implementation of high dimensional tensor networks running on NAND and NOR logic gates.

Anonymous at Sat, 9 Nov 2024 01:51:32 UTC No. 16467855

>>16467693
The nand logic exists at the hardware level, not the software level. From the truth table definition, of 1101 for imply and 1110 for nand, a transformation of string is not going to provide any advantage.
Anyways, if what you is saying is true, and you actually care, then you would draw the imp gate equivalence for each logic operation and find where transistor advantage is located.
Finally, P->Q = ~(P & ~Q), this is inherently a NAND gate.

Anonymous at Sat, 9 Nov 2024 01:55:10 UTC No. 16467858

>>16467855
>The nand logic exists at the hardware level, not the software level.
yes in Mr Williams's lecture he was quite clear that every component needs a redesign.

https://youtu.be/bKGhvKyjgLY?t=2455

here he states that one of the people in his lab wrote a compiler based on IMPLYs and found a 3x speed up over nand. and thats just by compiler thats not even hardwiring IMPLYs

Anonymous at Sat, 9 Nov 2024 02:09:14 UTC No. 16467873

>>16467858
Maybe there is some speed up in larger compound statement optimization, but then the statement is like
>a program optimized for imp ops is more efficient than one not optimized for nand ops.
It is very tough to prove this claim in general when imp is equivalent to nand.

Anonymous at Sat, 9 Nov 2024 02:40:56 UTC No. 16467890

>>16467873
well nand commutes, as opposed to Imply there different truth tables, Williams says you can mimic NAND with two IMPLY's .

what i'm quite curious about is what IMPLy's have to say about XOR