The physics and engineering required to last sufficiently long may be challenging. I hear it gets harder to power computers once the stars have long since burned out. As far as I know the physics isn’t settled yet.
That counterargument is a bit too general, since it applies not only to NP problems, but even to P problems (such as deciding whether a number is the GCD of two other numbers), or even any arbitrary algorithm modified by a few lines of codes such that its result is unaffected, merely delayed until after the stars burned out, or whatever limit we postulate.
For NP problems and e.g. P problems both, given how we understand the universe, there is only a finite number of inputs in both cases which are tractable, and an infinite number of inputs which aren’t. Though the finite number is well different for both, as a fraction of all “possible”, or rather well-defined (let’s avoid that ambiguity cliff) inputs, it would be the same.
Cue “We all live in a Finite State Machine, Finite State Machine, Finite State Machine …”
That counterargument is a bit too general, since it applies not only to NP problems, but even to P problems (such as deciding whether a number is the GCD of two other numbers), or even any arbitrary algorithm modified by a few lines of codes such that its result is unaffected, merely delayed until after the stars burned out, or whatever limit we postulate.
For NP problems and e.g. P problems both, given how we understand the universe, there is only a finite number of inputs in both cases which are tractable, and an infinite number of inputs which aren’t. Though the finite number is well different for both, as a fraction of all “possible”, or rather well-defined (let’s avoid that ambiguity cliff) inputs, it would be the same.
Cue “We all live in a Finite State Machine, Finite State Machine, Finite State Machine …”