You want the content of the paper to be carefully crafted. Bibtex entries are the sort of thing you want people to copy and paste from a trusted source, as they can be difficult to do consistently correctly.
steel-man means trying to interpret someone's argument in the most favorable light rather than arguing against a weaker interpretation. It does not mean making up a different argument for them that you like better.
That's not p hacking. That's just the nature of p values. P hacking is when you do things to make a particular experiment more likely to show as a success.
Why do you think senior managers would replace themselves if they could? Given the choice between saving a company and giving a senior manager slightly more money or power, the senior manager will always win.
If you do that, people outside the package can also do Username(x) conversions instead of calling NewUsername. Making value package private means that you can only set it from outside the package using provided functionality.
I don't think most people make a special trip just to get gas. It's usually a quick added stop along the way of another trip, which is less of a nuisance than having to make two small walks to move and plug/unplug your car.
They show the DFA for it on the site, it's 3 states. There's a starting state for the first . and then two states that transition back and forth between whether z was the last character or not.
I think what's actually happening here is that they're doing the intersection on the DFAs and then producing a regex from the resulting DFA. The construction of a regex from a DFA is where things get ugly and weird.
Having a constant runtime means there's a constant bound on the runtime, not that the runtime is an exact constant value. 100 + 1/n would still be constant, as it's bounded above and below by constants.
To have sub-constant time it would have to go to 0 as n increases, as otherwise we could bound the time below by a constant. This isn't possible, as a computer will take at least 1 time unit on every input. So the expected time will always be at least 1.
An algorithm can't have that property for its expected runtime, as it can only look at a sub-constant amount of the input of it runs in sub-constant time.
it's not possible for it to behave differently as n increases because it doesn't have enough time to distinguish between different values of n once it's large enough.
I'm not sure what your big-O expression is supposed to mean, but if a sequence is decreasing and bounded below (which runtime is) then it has a limit. Since the sequence is discrete, it can't get arbitrarily close to the limit without reaching it. So at some point the runtime will stop decreasing.
You can approximate the runtime with a function that decreases forever, but the actual runtime will be constant for large enough n.
> 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.
"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.
You can't have that because when N=K that's not a valid expression and when N>K you're putting a negative number in the big-O notation. You can't have negative runtime.
All algorithms have a lower-bound on runtime of 1. If a sequence is decreasing and bounded below, it converges to a value [1]. If the sequence is discrete, that means it reaches exactly that limit and never deviates from it.