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Flat origami is Turing complete (2023)

Flat origami is Turing complete (2023)

9 comments

·April 22, 2025
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gnabgib

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

gitroom

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

StopDisinfo910

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

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.

entaloneralie

If I may chip in, I wouldn't call it obvious or straight-forward, but multiset rewriting[1] can be implemented in terms of multiplication alone(like in Fractran), and multiplication can be implemented in origami[2], so there might be something there.

[1] https://wiki.xxiivv.com/site/pocket_rewriting

[2] https://wiki.xxiivv.com/site/paper_product.html

NooneAtAll3

> 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

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

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

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.