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esmi | 5 years ago

How about a 2 state 3 symbol Turing machine? That’s pretty simple, and universal too.

https://en.m.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol...

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order

tromp|5 years ago

It's not directly comparable, since this Turing Machine is not a self-interpreter in the sense of interpreting arbitrary programs in a language of Turing Machines.

esmi|5 years ago

First off, I admit I didn’t do my homework so I have no idea what I’m talking about, but couldn’t the Turing machine make a Turing machine interpreter and therefore be a self interpreter? It is universal, no?

arethuza|5 years ago

As tromp has a meta-circular implementation of lambda calculus maybe that Turing Machine could be implemented in lambda calculus and we could have an objective measure of which one is "simplest"?

tromp|5 years ago

It takes 829 bits of binary lambda calculus to interpret BrainFuck, which is very simple programming language modeled after Turing Machines. A self-interpreter in BrainFuck takes well over a thousand bits though [2]. Lambda calculus is not only very simple, but also very expressive. While combinatory logic, with only S and K, is even simpler than lambda calculus, and also has a trivial binary encoding (00 for S, 01 for K, and 10 for application), the shortest known self-interpreter is 263 bits, appreciably larger than for lambda calculus. My IOCCC entry [3] has more examples of the conciseness of binary lambda calculus.

[1] https://tromp.github.io/cl/Binary_lambda_calculus.html#Brain...

[2] https://arxiv.org/html/cs/0311032

[3] http://www.ioccc.org/2012/tromp/hint.html