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For example, you can solve the halting problem for bounded state size.
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If your bound is b, I am free to give you a machine that uses 2b storage, and you are hosed.Īnd none of the theorems about Turing machines or their equivalents apply unless the tape is truly unbounded. Which means *your* tape (or other storage) has to be big enough to represent *any* machine* I give you. The whole idea of Turing completeness doesn’t even work unless you have unbounded storage, because you’re meant to be able to simulate *any* Turing machine, regardless of the size of *its* tape. This is a simple distinction that you’re meant to get the first time somebody explains Turing machines. There can be *no* a priori limit on how large your tape *can* get. At any given moment, your tape is indeed of finite length… but you *always have to be able to go down to the store and by more tape*.
No, it doesn’t have to be infinite… but the machine has to be able to *add* as much tape as it wants any time it wants.
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Posted in Software Hacks Tagged conways game of life, game of life, python, turing complete Post navigation Check out the video below to truly get a sense of the scale of the machine that has devised. We’ve covered this field before and delved into this beautiful fringe of computer science. There are several other types of CA’s and the history behind them is fascinating. The Game of Life is an excellent example of Cellular Automaton (CA).
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This gives the computer four stages: execution, writing, increment PC, and write PC to memory. The clock is four loops, formed by the glider reflectors as the glider beams rotate. Instructions have a 4-bit opcode which is decoding in a few different instructions. The actual architecture has an 8-bit data bus, a 64-byte memory with two read ports, a ROM with 21 bits per line, and a one-hot encoded ALU supporting 8 different operations. While this isn’t the first computer in the Game of Life as published a design in 2000 and published a Spartan universal computer constructor in 2009, we think this is a particularly beautiful one. It’s all based on Golly, which is an excellent program for simulating Conway’s Game of Life, among other things. The Python includes scripts to assemble the basic programs as a bank of selectable glider generators.
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The basic building blocks are a period-60 gun, a 90-degree glider reflector, a glider duplicator, and a glider eater.Īll the Python code that generates these structures is on GitHub as the sheer size of the machine couldn’t possibly be placed by hand. This means the space between gates is crucial as signals need to be in phase alignment. Because two orthogonal gliders can cancel each other out or form a glider eater if they intersect with a good phase shift, the basic logic gates can be formed from these interactions. Unlike electricity, the Game of Life uses gliders as signals.
is one such individual who has created a computer in Conway’s Game of Life. Technically Microsoft PowerPoint, Portal 2, and Magic: the Gathering all are Turing-complete, what of it? Yet, each time someone embarks on an incredible quest of perseverance and creates a computer in one of these mediums, we stand back in awe. We often hear the term “Turing-complete” without giving much thought as to what the implications might be.
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