## Modern SAT solvers: fast, neat and underused (2018)

## Comments

` Solving Environment | / - | \`

The CNF Converter is a gem.

https://github.com/scala/scala/blob/v2.13.5/src/compiler/sca...

I had a lot of fun making my own CDCL solver in Rust, and I’ve really enjoyed messing with Z3 for some theoretical computer science. On all of my explorations, there was a very tangible problem size beyond which the solve time was unusable.

In the case of Z3 with most real world problems, the typical problem size is beyond this limit.

Modern SAT solvers are fast, neat and criminally *undertaught* by the universities. Seriously, why isn't this taught at the undergraduate level in CS70 [1] discrete math type courses or CS170 [2] analysis of algorithms type courses?

Boolean satisfiability problem

https://en.wikipedia.org/wiki/Boolean_satisfiability_problem

"In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE."

He has a few open source SAT solvers and tooling that provide good and proven examples on modern SAT solver techniques.

It's worth mentioning that there are higher level abstractions that are *far* more accessible than SAT. If I were teaching a course on this, I would start with either Answer Set Programming (ASP) or Satisfiability Modulo Theories (SMT). The most widely used solvers for those are clingo [0] and Z3 [1]:

With ASP, you write in a much clearer Prolog-like syntax that does not require nearly as much encoding effort as your typical SAT problem. Z3 is similar -- you can code up problems in a simple Python API, or write them in the smtlib language.

Both of these make it easy to add various types of optimization, constraints, etc. to your problem, and they're much better as modeling languages than straight SAT. Underneath, they have solvers that leverage all the modern CDCL tricks.

We wrote up a paper [2] on how to formulate a modern dependency solver in ASP; it's helped tremendously for adding new types of features like options, variants, and complex compiler/arch dependencies to Spack [3]. You could not get good solutions to some of these problems without a capable and expressive solver.

[0] https://github.com/potassco/clingo

[1] https://github.com/Z3Prover/z3

[2] https://arxiv.org/abs/2210.08404, https://dl.acm.org/doi/abs/10.5555/3571885.3571931

For example, what are the defining characteristics of a graphs for which the travelling salesman problem is resolvable without resorting to brute force?

https://github.com/darius/sturm/blob/master/satgame.py (Python 2)

This reminds me of make[0] and of being made aware that make[0] is a SAT solver. I think it was when I attended a conference. Unfortunately I cannot find an authoritative source to quote, so will rely on, and be grateful to, the HN community to correct me should this be wrong.

The Silent (R)evolution of SAT https://news.ycombinator.com/item?id=36079115