Patterns that didn’t change one generation to the next, Dr. To mark the 50th anniversary, the community - which hosts the LifeWiki, with more than 2,000 articles - created an Exploratorium, a large, explorable stamp-collection pattern. More trivially, the game attracted a cult of “Lifenthusiasts,” programmers who spent a lot of time hacking Life - that is, constructing patterns in hopes of spotting new Life-forms. The Game of Life motivated the use of cellular automata in the rich field of complexity science, with simulations modeling everything from ants to traffic, clouds to galaxies. Conway’s many other mathematical accomplishments, and he came to regard his missive to Mr. and output the new one, that the memory tape could also be a memory made out of logic gates, and finally that the read/write head could be something like a multiplexer and a binary counter, that allows to select a cell and to operate on it, and then to change the cell, to operate again etc.Life swiftly eclipsed Dr. If you really want to use TM to prove the T-completeness of GOL, you could say that the TM's transition table could simply be a set of logic gates, that takes the actual state etc. As you said, logic gates allows to compute any function, including all the possible $\lambda$-functions. If you spoke about $\lambda$-calculus, you will have said that it is equivalent to TM. evaluate any arbitrary logical function) another requirement? Or, is it an alternative requirement? Is the capability of implementing logical gates (i.e. beautiful examples (like cambrian explosion in golly)Īfter that, if you want to speak about the TM from the angle of T-completeness, I suggest you to also just show a bit of $\lambda$-calculus (or at least to speak about Church, for the Church-Turing Thesis), gif you have the time for that.(an infinite grid, some cells with 2 states, and then some rules) It's a simulation (kind of a game, but a no-player game).My habitual plan in order to present it is : Then, for GOL, I made multiple lectures, but as I'm French, I don't think you would like to see them. I think that your plan is good, but the most important is for it to be intuitive for you ! If you don't feel secure with it, just change it ! You can easily do a search like "nand logical completeness" to find the logic gate diagrams to show this.
NAND and NOR are each sufficient, on their own, to create every other logic gate. I have one further thought for you that might make your life simpler. So, it may be that you don't need to show how to simulate a TM in GoL nodes, but instead take a step to show that logical gates are sufficient to be Turing Complete. Thus, it stands to reason that, if you can imitate logical gates, you can create a Turing-Complete machine just as you would if you could simulate a Turing Machine. Here is a simple latch that stores which of the two input lines on the left turned on most recently: If you study memory, you begin by studying latches and flip-flops. Computer memory consists of logic gates that feed back into themselves. Multiplexers are basically just a bunch of AND gates. I can give you a simple(ish) example of each:įor the first requirement, processors can use multiplexers to create conditional jump options. The computer you typed this message onto is Turing Complete (well, sort of), yet the only tool it uses is logic gates. Here is a link to the pdf file of the report that I submitted, thanks for your suggestions! Which is the correlation between Turing-completeness and logical gates?.Is the capability of implementing logical gates (i.e.A way to read and write to some storage mechanismīut I never read anywhere about logical gates (or logical propositions in general).A form of conditional repetition or conditional jump (while, for, if and goto).that the necessary conditions for a system to be Turing-complete are: I have read dozen of times in StackExchange forums, papers, etc. The last point of the assignment asked me to prove the universality of Life by providing an implementation of logical gates in such model, and here come my doubts. Using such notions and based on previous works and papers, show how Life can be used to simulate a Universal Turing machine.Introduce the notion of Turing-completeness and its relation with computational universality.Introduce Turing machines, the notion of universality, and Universal Turing machines.I'm not required to actually build up a Universal Turing machine in Life, but rather I'm supposed to provide a step-by-step explanation of universality of GoL (as well as the meaning of such result). I was recently given an assignment at university asking me to discuss the universal computational capability of Conway's Game of Life.
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