# Solvers

# SAT Solvers

SAT Solvers are programs that can solve SAT (Satisfiability), an NP-complete program. SAT solvers typically take their input in the DIMACS format. That's hard to work with, so there are pre-processors that will convert a problem into DIMACS, give it to a SAT solver, and then convert the solution back to a specific problem domain. Such conversions are in P.

I've used the following SAT solvers successfully:

- picosat - easy to get working, but not very fast. Has the advantage that it can produce a list of all possible solutions out-of-the-box.
- glucose - like picosat, but fast. Does not have the ability to produce all possible solutions.
- Z3 - Can process DIMACS files.

I was not able to get these to work:

- minisat - just couldn't get it to compile.

I haven't used these:

- veriT-SAT - Can read DIMACS formatted SAT files.

# SMT Solvers

SMT solvers can work with higher level "theories" in math or logic. Because they can operate on logic directly, rather than converting everything into SAT, their models can be much more compact. More compact models may solve faster or slower, depending on the heuristics of the particular solver.

Most SMT solvers will take an input file in the SMT-LIB file format, which looks a lot like LISP. However, several of the SMT solvers also have a higher level API in Python or another language. People who are not familiar with LISP may find these APIs easier to work with

Getting started with SMT-LIB:

- First, start by looking at the Rise4Fun z3Tutorial with online solver.

- Next, download and skim the SMT-LIB Reference Manual. Most of it won't make sense for now, as it is very dense, but after you have read it a few times it begins to make sense.

- Next install a solver on your computer. I have found the Z3 is the easiest to use out of the box. You can download it from github, or you can install it for Python using pip.

One of the things you might want to do with an SMT-LIB file is to get the model (that is, the satisfying solution). You do that with the **(get-model)** command. One of the things that *I* want to do is to get all satisfying models. I have found these links useful for that:

I have put together a git repo of some of my very simple z3 scripts:

## Other solvers

*Yices* is another solver worth looking at. I’ll be doing that shortly:

*CVC4*

*MathSAT*

*veriT* is a prototype server currently under development

# Optimizers

Optimizers are special kinds of solvers that can optimize an objective function. Convex linear optimizers that can work with floating point numbers are relatively fast, as linear programming is in P, but requiring an integer solution makes finding some problems tricky and creates an NP-hard problem. [1]