SAT is a NP-complete problem also called "satisfiability problem". It is most often presented in the form of a set of boolean clauses, each of those being a disjunction of literals. A literal is either a proposition or its negation. The problem goal is to find whether it exists a valuation for those boolean literals such that all clauses are true, and, in this case, to give such a valuation. In other words, can we give each proposition a truth value such that all clauses have at least one true literal?
A simple example is:
a or (not b)
b or c
(not a) or (not c)
(not c)
which is satisfiable by the valuation a=1, b=1, c=0
There exists a simple, straighfoward standard format used to facilitate reading of a problem by a solver.
It is composed of:
'c')p <n> <n>. The
two numbers define the number of variables (propositions)
and the number of clauses, respectively.-9 represents the literal (not x9) where x9 is the
ninth proposition. A positive number just represents a
proposition. Each clause (a list of literals) is ended by a
0, which cannot be a proposition since there would be no way
to tell x0 from (not x0).Another example:
c a very personal comment on this problem
c talking about clauses and literals
p 3 2
1 2 3 0
2 -3 0
It represents the logical problem
x1 or x2 or x3
x2 or (not x3)
A list of a few problem (quite) simple on which to test a SAT-solver, in Dimacs format.
I adapted some code from ratsat, itself a port of minisat.
The result is a SAT solver in rust, batsat with the ability to provide callbacks. I think these should be enough to be the basis for a CDCL(T) SMT solver.
I have been working on a (relatively) efficient SAT-solver written in Java. It implements the DPLL algorithm, with the following features:
Some lacking features are: