The Nineteenth Byte

Q: Tribute to John Conway: Collatz in FRACTRAN

12:24 AM

Having no challenges today makes me feel bored. I need to Sandbox one.

New Main Posts

12:58 AM

John Horton Conway was a brilliant mathematician. Among his contributions were three Turing-complete esolangs: Game of Life (esolangs wiki), FRACTRAN (esolangs wiki), and Collatz function (esolangs wiki). Because we did an extremely amazing job around GoL, it is time for the challenge with the o...

2 hours later…

2:41 AM

The single question on Conway's works is giving LOTS of topics to code-golf in.

2 hours later…

4:37 AM

Penney-Conway average odds code-golf math probability-theory combinatorics Background Penney's game is a two-player game about coin tossing. Player A announces a sequence of heads and tails of length \$n\$, then player B selects a different sequence of same length. The winner is the one whose s...

1 hour later…

Lyxal

5:46 AM

I almost forgot that today is 4/20/20 in American date formats. Nice

Too bad there's no 20/20/20.

6:05 AM

I am terrible at these puzzles for young kids. What fraction of the square is
https://ichef.bbci.co.uk/images/ic/832xn/p089bm50.png

Perimeter of Conway hexagon code-golf geometry trigonometry Background Given a triangle \$ABC\$, extend its three sides by the opposite side length, as shown in the figure below. Then the six points surprisingly lie on a circle called the Conway circle, whose center coincides with the incenter....

H.PWiz

@Anush The central triangle is 3/8 of the square

How do you get that?

6:20 AM

@Anush Imagine the center point of the square, and connect it with the three vertices of the triangle. Then you get three small triangles which have 1/2 base and 1/2 height (1/8 area of the square). 1/8 + 1/8 + 1/8 = 3/8.

Or just sum the three shaded areas separately...

Your second method is really simple!

Harder method: Pick the upper left side as the base. Then it has base sqrt(2) * 1/2 and height sqrt(2) * 3/4.

Now I understand your first method too. Thank you!

3 hours later…

9:41 AM

:54133417 Thanks

@dzaima thank you

10:00 AM

hi all

hi!

Most of my messages are now posted to the NST chat. It probably doesn't lead to criticisms, because I'm the only active person there.

NST?

Pi

A chatroom for Pi enthusiasts (primarily discussing Pi calculus)

@Anush NST is basically a chat for teaching/golfing in the (Naive) Set Theory.

Interested in golfing in the Set Theory?

no, but thanks

I am interested only in subset construction right now

10:21 AM

@Anush What for?

converting an NFA to a DFA

the algorithm is simple in theory

the tricky part is making it fast

I am very tempted to pose it as a challenge. The only difficulty is checking if the answers are right

Beta Decay

10:38 AM

pastebin.com/nrP1SAq1

Can anyone see why this is throwing a "mismatched brace" errir

*error

@ChristianSievers When you are about, I think I am ready to learn how you created the NFA. I have read more about NFA to DFA conversion so I am in a better position than before

11:01 AM

CMC Write down 7 consecutive numbers so that the digit 2 is used exactly 16 times.

Infinitely many solutions then.

you only need to write down one of them

@Anush 2215 2216 2217 2218 2219 2220 2221

nice :)

Found with {16=+/'2'=⍕⍵:⍵⋄∇1+⍵}⍳7 in APL. Try it!

dzaima

11:06 AM

@Adám imo ⍣ is much clearer here

@dzaima Our solutions might make good material for the APL Cultivation.

@Anush I don't know what more to say than I did in my math.SE answer (except there is a bug in the pseudocode). NFA to DFA conversion is not needed for understanding the NFA.

@Anush All of them :-)

@Anush Fixed.

11:31 AM

CMC: Given an input n, output the smallest two-number pair which uses n 1's.

I will reread that answer. May I ask then if I am still stuck?

11:46 AM

@Anush Sure

@Adám isn't there an answer is the 200s?

in the 200s

@Anush There can't be. The most you can get is 15, no? 220 221 222 223 224 225 226

1 hour later…

12:58 PM

@Adám Ah yes. I was solving 8 consecutive numbers :)

@Anush The necessary change to my code should be obvious.

tryapl.org/?a=%7B16%3D+/…

1:22 PM

Making a programable computing chip Make a programable chip with 8000 commands ROM and 48 16-bit unsigned words RAM initalized with zero. These commands should be supported: a = b + c # mod 65536 a = b - c a = b * c a = b / c # undefined behavior if c==0 a = b % c a = b > c # return 0 or ...

@petStorm snap!

@Anush snap!

1:49 PM

@ChristianSievers can you think of any way an NFA to DFA conversion question could be posed where we could check the correctness of the outputs?

I just downloaded Scratch 1.1. It has no support for lists... it's useless!

en.scratch-wiki.info/wiki/List ?

I'm going to delete it after all after wasting 10 minutes on downloading it.

The green flag and the stop sign are both enormous, it make me think as if I'm on mobile (which I'm not).

Scratch it.

2:07 PM

@Anush Checking that automata accept the same language is possible. I wonder if there would be any interesting answers that don't just call a library, especially if you make it a fastest-code challenge

@ChristianSievers I have looked and it seems that a) there is scope for parallelisation and data structure improvement sand b) there seem to be no free libraries that already do them

at least that I could see

1 hour later…

3:28 PM

@ChristianSievers In math.stackexchange.com/questions/3498630/… I am not sure what head and tail mean. If l = abcd add r = abdc, does head(l) = a and tail(l) = d? Also, when it says "When both heads are behind the words" what does it mean to be behind l? Is that before 'a' or after 'd'?

@Anush tail(l)=bcd, behind the word: after d (if we agree to start at a), it's when we have worked through all the input

thanks. Isn't the word behind the head after d?

if you are going from left to right

@ChristianSievers Are we to interpret L_{c, w} as the state where the current edit distance is c and we have read in |w| more characters from the left string than the right string?

I'm not sure what your question is. But note that head has two meanings here: head of a list: first element. And the reading head of a machine that operates with tapes.

@ChristianSievers It's not important. I was just confused by the use of the word "behind". I would have thought that at the end both heads would be "in front" of the words as they are going forwards.

At the end, the reading head has passed the word and is behind it

3:43 PM

It's just a question of language so I am happy to agree.

no sorry... L_{c, w} is the state with edit distance c and w remaining in the left string?

About L_{c,w}, c is the current edit distance of the right word read so far, and the left word without the letters of w. It corresponds to a situation when the left reading head is behind the right one. It's exactly the same c as in the pseudocode

does "behind" here mean more of the left string has been read in (than the right string) or less?

less

thanks

(unless I also mixed it up in other places. I do get confused which I called L and which I called R)

In other word: the automaton has read more of the left string than the first machine or the pseudocode algorithm would have read from it, so what was read too early is memorized in the state

1 hour later…

5:11 PM