Catalytic computing taps the full power of a full hard drive
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Catalytic computing taps the full power of a full hard drive
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Re: Catalytic computing taps the full power of a full hard drive
#2Found the original paper outside of the paywall:
https://iuuk.mff.cuni.cz/~koucky/papers/catalytic.pdf
The ~koucky/papers/ root is also a goldmine of papers, including another catalytic one.
Re: Catalytic computing taps the full power of a full hard drive
#3So the trick is to do the computation forwards, but take care to only use reversible operations, store the result outside of the auxiliary "full" memory and then run the computation backwards, reversing all instructions and thus undoing their effect on the auxiliary space.
Which is called catalytic, because it wouldn't be able to do the computation in the amount of clean space it has, but can do it by temporarily mutating auxiliary space and then restoring it.
What I haven't yet figured out is how to do reversible instructions on auxiliary space. You can mutate a value depending on your input, but how do you use that value, since you can't assume anything about the contents of the auxiliary space and just overwriting with a constant (e.g. 0) is not reversible.
Maybe there is some xor like trick, where you can store two values in the same space and you can restore them, as long as you know one of the values.
Edit: After delving into the paper linked in another comment, which is rather mathy (or computer sciency in the original meaning of the phrase), I'd like to have a simple example of a program that can not run in it's amount of free space and actually needs to utilize the auxiliary space.
Re: Catalytic computing taps the full power of a full hard drive
#4This is very similar to an old approach to LISP garbage collection. All of memory is a tree of small cells. You need to walk the the tree and don't have space for a stack of the links that got you to where you are. So you store the backlinks in the forward links by XORing the forward link with the backlink. As the tree-walker backs down the tree, the links are XORed again, restoring the forward link.
Re: Catalytic computing taps the full power of a full hard drive
#5So the trick is to do the computation forwards, but take care to only use reversible operations, store the result outside of the auxiliary "full" memory and then run the computation backwards, reversing all instructions and thus undoing their effect on the auxiliary space. Which is called catalytic, because it wouldn't be able to do the computation in the amount of clean space it has, but can do it by temporarily mut…
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Re: Catalytic computing taps the full power of a full hard drive
#6If I give you a hard drive full of photos, you could compress them, use the excess hard drive space for your algorithm, then uncompress the photos and give a full hard drive back to me. Is that’s what’s going on here?
Basically it’s exploiting unused channel capacity of the memory if the Shannon entropy isn’t maxed out?
Re: Catalytic computing taps the full power of a full hard drive
#7If I give you a hard drive full of photos, you could compress them, use the excess hard drive space for your algorithm, then uncompress the photos and give a full hard drive back to me. Is that’s what’s going on here? Basically it’s exploiting unused channel capacity of the memory if the Shannon entropy isn’t maxed out?
They are explicitly not assuming anything about the content of the auxiliary space (full hard drive).
So the data might be incompressible and thus compressing it and restoring it afterwards would not work.
Edit: From the paper:
> One natural approach is to compress the data on the hard disk as much as possible, use the freed-up space for your computation and finally uncompress the data, restoring it to its original setting. But suppose that the data is not compressible. In other words, your scheme has to always work no matter the contents of the hard drive. Can you still make good use of this additional space?
Re: Catalytic computing taps the full power of a full hard drive
#8So the trick is to do the computation forwards, but take care to only use reversible operations, store the result outside of the auxiliary "full" memory and then run the computation backwards, reversing all instructions and thus undoing their effect on the auxiliary space. Which is called catalytic, because it wouldn't be able to do the computation in the amount of clean space it has, but can do it by temporarily mut…
Just run it twice and XOR the relevant bits each time, so the second pass flips them back?
Re: Catalytic computing taps the full power of a full hard drive
#9So the trick is to do the computation forwards, but take care to only use reversible operations, store the result outside of the auxiliary "full" memory and then run the computation backwards, reversing all instructions and thus undoing their effect on the auxiliary space. Which is called catalytic, because it wouldn't be able to do the computation in the amount of clean space it has, but can do it by temporarily mut…
for me, perfect introduction to catalytic computing was this lecture: https://www.youtube.com/watch?v=_KEORzRpxY8
Re: Catalytic computing taps the full power of a full hard drive
#10If I give you a hard drive full of photos, you could compress them, use the excess hard drive space for your algorithm, then uncompress the photos and give a full hard drive back to me. Is that’s what’s going on here? Basically it’s exploiting unused channel capacity of the memory if the Shannon entropy isn’t maxed out?
it is indeed one of important techniques in catalyitic computing that either 1)you can compress the catalyst, giving you space or 2)uncompressible catalyst gives you a source of randomness