Sorry if that made no sense. Basically, if a language can interpret itself, does that show that it's TC?
I've been on the lookout for a UTM description, and I've found a machine with only 2 states and 3 symbols. I thought, how neat, it's so simple! I put the description into a TM simulator, realized I had no idea how to use the rule set, and took to the internet again to figure out why. Turns out, it simulates a 1D CA, which I know to be terribly time and space inefficient, and very hard to understand. It makes me wonder if there's a larger, synthetic ruleset, one with more internal states but only 3 symbols (1, 0, and empty symbol), one that can reasonably be experimented with, one that can be programmed more easily?
If I understood it correctly, a universal turing machine can simulate any turing machine with any input. For it to be turing complete, it has to be able to simulate any turing machine, therefore UTM must be turing complete by default?
If that's the case, why have the distinction? Feel like I must be missing something here.
The universe seems to be a very complex, Turing-complete machine- the fact that we can build Turing machines implies that the universe is (at least) Turing-complete. This makes me wonder- could the universe itself be simulated on an extremely powerful Turing machine? If so, is it *actually* being simulated on such a device? How would we know?
Hi everyone,
I am playing recently with CA. One of the things that I read is that it can represent a universal turing machine (for 1-D with 2 colors - if I didn't misunderstood). But I am having a hard time imagining how something practical can come out of this.
For example, if I want to build a simple binary classifier using CA, for a sequence of zeros and ones, to determine if the number of ones is odd or even. How to input data to CA? (is it the initial row?) where to catch the output? What are we trying to do exactly (e.g, finding a rule for CA)?
I am quite confused...
Also, is there an actual application of CA at the moment? (beside the pretty graphics it generates)?
A research team from Google Research, University of Cambridge and Alan Turing Institute proposes PolyViT, a single transformer model capable of processing multiple modalities and datasets. PolyViT is parameter-efficient and learns representations that generalize across multiple domains.
Here is a quick read: Google, Cambridge U & Alan Turing Institute Propose PolyViT: A Universal Transformer for Image, Video, and Audio Classification.
The paper PolyViT: Co-training Vision Transformers on Images, Videos and Audio is on arXiv.
Rule 110 was proven universal by Cook (Universality in elementary cellular automata. Complex Systems, 15(1):1– 40, 2004).
If I have a machine that can, given a 3-cell input, produce the correct output for the next time step for the middle cell according to Rule 110, is that sufficient proof that the machine is universal? (The machine could easily be duplicated arbitrarily many times to operate on an arbitrarily large number of cells.)
Or do I also need to demonstrate the capacity of the machine to reorient to any arbitrary location on the plane of cells?
(Obvious newbie here, trying to figure out if I have something special. Thanks for any help.)
Hi!
I was given a research task to construct a single tape Universal Turing Machine. I've read a couple of papers (like this one (pdf) and this one (pdf)) and skimmed tens of them, but they either don't give the final description of the machine so I cannot check it for correctness, or I don't understand the way the input is given to them.
In the second linked paper, I don't understand the input specification, specifically the encoding of a configuration. It says the following:
...ccc<B>S*G(<A>N)*(<A>N<E>U<E><A>N)(<A>N)*Dccc...
For U(5,5), I believe it should mean this:
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ccc - used for separation
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<B> - describes the whole transition table
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S* - (d^2)* -> zero or more repititions of dd
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G - epsilon (does this denote an empty sequence or is it just a character from the alphabet?)
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<A> - I have no clue how is this supposed to be encoded.
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N - delta
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<E> - as with <A>, I don't really know what it means
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D - epsilon (the same as for G, is it an empty sequence or a character from the alphabet?)
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H - c d delta
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V - delta
For <a(i)>, does b^4i-1 mean bbb for a(1), bbbbbbb for a(2), etc.?
The other paper gives a good description of input and the way the machine solves the problem, but it does not give the final program.
I have written a Python simulator for any single tape UTM.
If you know a resource where I can learn more about a universal turing machine with a single tape (hopefully with a nice description of input and the final program), I would be really greatful.
Thank you very much!
EDIT: After hours of investigation, I found Minsky's 7-state 4-color machine. I do not know, however, how to setup the tape for it (in other words, what is the machine's input), and I can't find that info anywhere.
This is an automatic summary, original reduced by 97%.
> To solve any NP problem using our NUTM, one would first translate the problem into an initial string of Thue symbols, then determine the Thue string(s) that signals the accepting state-such a translation is always possible as the Thue system is universal.
> DNA computingWe use DNA computing to implement a Thue NUTM. Like other forms of molecular computing, DNA computing trades space for time: 'there's plenty of room at the bottom'.
> The use of Thue systems overcomes many problems with existing DNA computing designs.
> Implementation of a DNA non-deterministic universal Turing machineIn our NUTM starting states and accepting states are sequences of DNA that encode strings of Thue symbols.
> Taken together, these results demonstrate that all the Thue rules required for an NUTM can be physically implemented using DNA mutagenesis.
> The complexity class PSPACE consists of those problems that can be solved by a Turing machine using a polynomial amount of space.
Summary Source | FAQ | Theory | Feedback | Top five keywords: problem^#1 NUTM^#2 Thue^#3 DNA^#4 rule^#5
Post found in /r/Futurology, /r/programming, /r/technology, /r/realtech, /r/science, /r/thisisthewayitwillbe, [/r/BitcoinAll](http://np.reddit.com/r/BitcoinAll/comments/5x23ho/implementing_a_nondeterminis
... keep reading on reddit ➡UTMs can simulate any arbitrary Turing machine, but can one simulate another? And would it even be useful, either conceptually or practically?
This paper I came across suggests that if a computing device can only perform 'n' operations per unit time, you can always create a real-time/interactive computation problem requiring 'n+1' operations per unit time. This idea was used to prove that there cannot be a practical universal computer.
I read somewhere that Turing Machines can only be used to compute functions for which the input is completely pre-specified. Is this true?
Paper: https://www.cs.auckland.ac.nz/~cristian/universal.pdf
