This article was first published on RChain Cooperative - Medium
Greg Meredith discusses calculating the square root with Isaac DeFrain and Christian Williams. Scroll down for the transcript, which is after the slides.
Greg: The idea goes way back for me — about 17 years. I was hanging out in Harvard, waiting to chat with Walter Fontana and another process Algebraist, just who was interested in biology. To entertain myself, I was looking at analogs of arithmetic operators. It turns out that you can define an analog of the notion of square root. For the process calculi, there’s this notion of running processes in parallel. You have an equational notion of equivalence called bisimulation. You can ask the question: Is there a process square root of P such that square root of P par square root of P is bisimilar to P. You can give a crisp definition of this operation.
With pi, I was unable to come up with a calculation for the square root. If you turn to your calculator on your phone or laptop, you can press a button and it will calculate the square root of a number. The question is: Could you calculate the square root of a process?
All this was just good mathematical fun. I really didn’t think about it as having an import with respect to computation. It turns out it does. It’s easier to see if you consider nth roots rather than just square roots.
The generalization is fairly straightforward. The nth root of process P — written just nth root P — if you put N copies of the nth root P in parallel with each other, that’s bisimilar to P. You can see that this is starting to look remarkably like the kind of thing that we expect of Casper in RChain. We’re running ...
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