Here, /sci/ I've identified a problem and I want to know

>>7671594
>Continued in the next post.
Why.

File: daber.jpg (48KB, 640x370px) Image search: [Google]

48KB, 640x370px

That picture is ridiculous. The orthodox Jews condemn the Zionist government that is currently in place in Israel at the moment.

File: Rule110Big.jpg (39KB, 265x266px) Image search: [Google]

39KB, 265x266px

>>7671594
First of all, I'll identify the roots of the problem.

Rule 110 (pictured) is an elementary cellular automaton that was conjectured by Stephen Wolfram to be Turing-complete, and later proven to be complete by his assistant Matthew Cook. In Wolfram's own classification of cellular automata, it is a Class 4 rule.
Cook showed it was able to simulate another Turing-complete program, a cyclic tag system.

Rule 110 is called such because it's rule:

[math]\begin{matrix}
111 & 110 & 101 & 100 & 011 & 010 & 001 & 000\\
0 & 1 & 1 & 0 & 1 & 1 & 1 & 0
\end{matrix}[/math]

Can be simplified into the binary string

01101110

Which is equivalent to 110 in Base 10.

This will be important in the next post

>>7671602
To keep it bumped and garner some interest.
>>7671604
It's the only picture I had on hand. I do agree though.
>>7671606
Continued here. This is officially original research after this.

Let's split up the rule to cases where the center cell, which we will call c, is 1, and where it is 0. I'll format these tables a bit differently than above.

For c = 1:

[math]
\begin{vmatrix}
00\\
01\\
10\\
11
\end{vmatrix}\left.\begin{matrix}
1\\
1\\
1\\
0
\end{matrix}\right|
[/math]

For c=0:

[math]
\begin{vmatrix}
00\\
01\\
10\\
11
\end{vmatrix}\left.\begin{matrix}
0\\
1\\
0\\
1
\end{matrix}\right|
[/math]

We find that for c = 1, it is equivalent to a NAND operator, and for c = 0, it is equivalent to the truth table of q (the right side).

Now we know that NAND is a functionally equivalent operator, meaning using only NAND gates we can construct all other Boolean truth tables within the system.

Now it is easy to think that this is related to it's Turing-completeness. So let's test that.

>>7671604
>The orthodox Jews

Some orthodox Jews condemn Zionism and other's don't...

>>7671619
There is only one other binary Boolean operator that is functionally complete, the NOR gate. So let's construct a copy of Rule 110, but replace NAND with NOR.

For c=1:

[math]
\begin{vmatrix}
00\\
01\\
10\\
11
\end{vmatrix}\left.\begin{matrix}
1\\
0\\
0\\
0
\end{matrix}\right|
[/math]

For c = 0:

[math]
\begin{vmatrix}
00\\
01\\
10\\
11
\end{vmatrix}\left.\begin{matrix}
0\\
1\\
0\\
1
\end{matrix}\right|
[/math]

Let's translate this back into a rule:

[math]
\begin{matrix}
111 & 110 & 101 & 100 & 011 & 010 & 001 & 000\\
0 & 0 & 1 & 0 & 0 & 1 & 1 & 0
\end{matrix}
[/math]

00100110 in decimal is 38. Let's look at Rule 38 on Wolfram|Alpha...

File: nnn.png (30KB, 361x183px) Image search: [Google]

30KB, 361x183px

>>7671630
...Oops. It's a class 2 rule that doesn't seem to be Turing-complete. So let's take the scenarios here:

1. Rule 110's Turing-completeness is completely unrelated to the fact it encodes a functionally-complete Boolean operator.

2. Rule 38 is Turing-complete, and Wolfram's classifications aren't as useful as breaking rules up into their Boolean constituents.

So /sci/. What do you think is more likely?

>>7671635
No one has any idea what you're talking about, sorry.

>>7671604
YES GOYIM
JEWS ARE GOOD

>>7671604
LOL that's what you think makes the pic ridiculous?

Anyway, only a small fringe group of orthodox campaign against Israel like in your pic.

baka desu senpai

>>7671635
Sorry anon but I'm familiar with rule 110 only to the extent that it can be used to prove a language is Turing complete.

>>7671635
A Turing complete rule can encode a non-Turing complete rule, there's no reason for this not to be the case. Rule 38 is not Turing complete. Also, replacing a rule with a similar but fundamentally different rule and getting a different result should be unsurprising

>>7671635
Propositional logic isn't Turing complete, so I don't see how encoding NAND/NOR has anything to do with it.

Also, has /sci/ finally gotten support for matrices? I've been away for too long.

[eqn]\begin{pmatrix} s & m & h \\ t & b & h \\ f & a & m\end{pmatrix}[/eqn]

>