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by daveFNbuck 1030 days ago
"constant time" in complexity theory just means there's a constant bound on runtime. It doesn't have to actually have the exact same runtime down to the instruction for every input. Here, the bound would be a quadrillion.

Of course, showing a constant upper-bound doesn't tell us that it isn't even faster than constant as in the proposition I was responding to. That's why I focused on the constant lower-bound.
1 comments
Dylan16807 1030 days ago
I know what it means, and I stand by it being limited to the point of misleading in a case like this.

Running any (halting) algorithm on a human computer is constant time, because you're bound by the number of states you can fit into some terabytes, but nobody should actually try to use that as a final analysis.

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daveFNbuck 1030 days ago
> Running any (halting) algorithm on a human computer is constant time, because you're bound by the number of states you can fit into some terabytes, but nobody should actually try to use that as a final analysis.

That's the sort of thing I would usually say to explain why we do things like use asymptomatic analysis and ignore polynomial factors. If you have a different solution, that's great, but you're no longer taking about the kind of runtime the article is about.

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Dylan16807 1030 days ago
It depends on how abstract you want to be. You shouldn't always shove the lever all the way to the most abstract single value.

My suggested solution is "don't delete all nuance". If the runtime doesn't behave nicely, give that a mention. Most things do behave nicely, so that's not much of a burden.

> the kind of runtime the article is about

The article spends plenty of time talking about computational feasibility, which is not about the limits as you approach infinity.

It even equates P with "trivial", which is... not good.

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