Flat origami is Turing complete (2023)

https://arxiv.org/abs/2309.07932

by PaulHoule • 1 year ago

40 12 1 year ago

arxiv.org

gnabgib• 1 year ago

Related How to Build an Origami Computer (63 points, 2024, 15 comments) https://news.ycombinator.com/item?id=39191627

NooneAtAll3• 1 year ago

we prove that flat origami, when viewed as a computational device, is Turing complete, or more specifically P-complete

...aren't those mutually exclusive?

I feel a mix of "those are obviously different complexity levels" and "is it like C pre-processor turing-completeness situation?"

lambdaone• 1 year ago

My understanding of this is that P-completeness for a problem implies that any problem in P can be transformed into it with a polynomial-time reduction. Deterministic Turing machines (more precisely, the problem of determining the future state of a deterministic Turing machine) are in P.

tromp• 1 year ago

Not with a polynomial-time reduction though. Quoting from [1]:

Generically, reductions stronger than polynomial-time reductions are used, since all languages in P (except the empty language and the language of all strings) are P-complete under polynomial-time reductions.

[1] https://en.wikipedia.org/wiki/P-complete

cartoffal• 1 year ago

Turing completeness and P completeness are completely different things. There is no sense in which P-completeness is a "more specific" version of Turing-completeness.

gitroom• 1 year ago

Honestly wild how you can get Turing completeness outta folding paper, never thought I'd read that today.

StopDisinfo9102• 1 year ago

That's why I have always prefered Church approach to computation to Turing machines.

The lambda calculus, by its simplicity as just a rewriting language, makes it "obvious" how effective computability emerges from very little.

yorwba• 1 year ago

The reduction in the article boils down to origami crease patterns simulating rule 110 simulating a cyclic tag system simulating a clockwise Turing machine simulating an arbitrary Turing machine (and specific Turing machines simulating the lambda calculus are known).

Do you think there is an "obvious" way to simulate the lambda calculus using origami crease patterns more directly? For example, a cyclic tag system or even rule 110 configuration simulating the lambda calculus without indirection through Turing machines.

PaulHoule• 1 year ago

It's a big controversy in CS education, isn't it?

Knuth's Art of Computer Programming was built around assembly language for a fantasy computer which is inspired more or less by the Turing machine (program counter is an index into a program 'state', instructions transform a data 'state' and transition to a different program 'state') whereas Structure and Interpretation of Computer Programs is more inspired by Church.

The pinnacle of undergraduate CS education, I think, is compilers, which is where those approaches are ultimately unified on a practical level (you make a machine that transforms one to the other) but the introductory course for the non-professional programmer or the person who aspires to writing compilers someday is still pretty controversial.

entaloneralie2• 1 year ago

Related: Origami-Constructible Numbers[1] & Folding Primes[2]

[1] https://www.cs.mcgill.ca/~jking/papers/origami.pdf

[2] https://www.pythabacus.com/Origami%20Fractions/folding.htm

Flat origami is Turing complete (2023)

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