Comment by almostgotcaught

> To me an algorithm is closed

i dunno what "closed" means here? converges? lots of things with heuristics converge...

most things people think of as algorithms are just heuristics codified. take for example unit propagation in DPLL (fairly modern SAT approach); quoting wiki[1]

> In practice, this often leads to deterministic cascades of units, thus avoiding a large part of the naive search space.

that *in practice* there means there's no guarantee because ofc not - otherwise they would've proven something about NP. but they didn't, they just came up with a way to search that's sometimes/often not bad. a lot of people call this an algorithm ("... is a refinement of the earlier Davis–Putnam algorithm") because it fits the dictionary definiton (a repeatable process) but i do not because it's a repeatable process that isn't proven to produce anything (ie faster than brute force). and the intuition i'm proposing for why it doesn't is because it doesn't actually shrink the search space fast enough.

note, my definitions/intuitions don't translate/have the same force elsewhere (especially in continuous/differentiable spaces) but they're a pretty standard/obvious perspective in combinatorial optimization (np-hard/np-complete problems).

[1] https://en.wikipedia.org/wiki/DPLL_algorithm#The_algorithm