I've always been fascinated by how linear programming seems to be applicable to every problem under the sun but SAT solvers only really seem to be good at Sudoku.
In practice that are a bunch of problems that seem to be SAT, but they are either SAT at a scale where the solver still can't find a solution in any reasonable time or they turn out to not really be SAT because there is that one extra constraint that is quite difficult to encode in simple logic.
And it is unrewarding experimenting because it ends up being a day or so remembering how to use a SAT solver, then rediscovering how horrible raw sat solver interfaces are and trying to find a library that builds SAT problems from anything other than raw boolean algebra (the intros really undersell how bad the experience of using SAT solvers directly is, the DIMACS sat file format makes me think of the year 1973), then discovering that a SAT solver can't actually solve the alleged-SAT problem. Although if anyone is ever looking for a Clojure library I can recommend rolling-stones [0] as having a pleasant API to work with.
> ... SAT solvers only really seem to be good at Sudoku.
This is really not true.
SAT solvers are really good these days, and many (exact) algorithms (for NP-hard problems) simply use some SOTA SAT solvers and are automatically competitive.
I love SAT solvers, but way more underappreciated by software engineers are MILP solvers.
MILPs (Mixed Integer Linear Programs) are basically sets of linear constraints, along with a linear optimization functions, where your variables can either be reals or ints.
Notably, you can easily encode any SAT problem as a MILP, but it's much easier to encode optimization problems, or problems with "county" constraints as MILPs.
Both are severely underused for sure. But it didn't help that for a long time open source MILP solvers were pretty mediocre.
HiGHS didn't exist, SCIP was "non-commercial", CBC was ok but they've been having development struggles for awhile, GLPK was never even remotely close to commercial offerings.
I think if something like Gurobi or Hexaly were open source, you'd see a lot more use since both their capabilities and performance are way ahead of the open source solutions, but it was the commercial revenue that made them possible in the first place.
Using CP-SAT from Google OR-Tools as a fake MILP solver by scaling the real variables is pretty funny though and works unreasonably well (specially if the problem is highly combinatorial since there's a SAT solver powering the whole thing)
SATs are cool but MILPs are cooler IMO.
Lol I've been trying to train a neural network over a finite field, not the reals and oh my god MILPs are God's gift to us.
Problems, including NP-complete ones, are only a product of the way you look at them and the reference frame from where you look at them. They get their incarnation only out of the observer's context.
I've always been fascinated by how linear programming seems to be applicable to every problem under the sun but SAT solvers only really seem to be good at Sudoku.
In practice that are a bunch of problems that seem to be SAT, but they are either SAT at a scale where the solver still can't find a solution in any reasonable time or they turn out to not really be SAT because there is that one extra constraint that is quite difficult to encode in simple logic.
And it is unrewarding experimenting because it ends up being a day or so remembering how to use a SAT solver, then rediscovering how horrible raw sat solver interfaces are and trying to find a library that builds SAT problems from anything other than raw boolean algebra (the intros really undersell how bad the experience of using SAT solvers directly is, the DIMACS sat file format makes me think of the year 1973), then discovering that a SAT solver can't actually solve the alleged-SAT problem. Although if anyone is ever looking for a Clojure library I can recommend rolling-stones [0] as having a pleasant API to work with.
[0] https://github.com/Engelberg/rolling-stones
> ... SAT solvers only really seem to be good at Sudoku.
This is really not true.
SAT solvers are really good these days, and many (exact) algorithms (for NP-hard problems) simply use some SOTA SAT solvers and are automatically competitive.
[delayed]
I love SAT solvers, but way more underappreciated by software engineers are MILP solvers.
MILPs (Mixed Integer Linear Programs) are basically sets of linear constraints, along with a linear optimization functions, where your variables can either be reals or ints.
Notably, you can easily encode any SAT problem as a MILP, but it's much easier to encode optimization problems, or problems with "county" constraints as MILPs.
Both are severely underused for sure. But it didn't help that for a long time open source MILP solvers were pretty mediocre.
HiGHS didn't exist, SCIP was "non-commercial", CBC was ok but they've been having development struggles for awhile, GLPK was never even remotely close to commercial offerings.
I think if something like Gurobi or Hexaly were open source, you'd see a lot more use since both their capabilities and performance are way ahead of the open source solutions, but it was the commercial revenue that made them possible in the first place.
Using CP-SAT from Google OR-Tools as a fake MILP solver by scaling the real variables is pretty funny though and works unreasonably well (specially if the problem is highly combinatorial since there's a SAT solver powering the whole thing)
SATs are cool but MILPs are cooler IMO. Lol I've been trying to train a neural network over a finite field, not the reals and oh my god MILPs are God's gift to us.
Problems, including NP-complete ones, are only a product of the way you look at them and the reference frame from where you look at them. They get their incarnation only out of the observer's context.