SAT solving

Boolean satisfiability

Abbreviated SAT

The problem of deciding whether a Boolean formula has a satisfying assignment.

Definition

Boolean satisfiability

Boolean satisfiability (SAT) asks whether any assignment makes a Boolean formula true.

SAT is a basic decision problem in computer science. Modern solvers can decide formulas with millions of literals by combining propagation, decisions, conflict analysis, and learned clauses.

01

Example

The formula (a or b) and (not a or b) is sat because b = true satisfies both clauses.

02

Important distinction

SAT variables are Boolean. Arithmetic structure must be encoded into Boolean constraints or handled by an SMT solver.

After reading this article, you should be able to

  • Define SAT in the sense used on this site.
  • State a SAT problem and interpret sat, unsat, and unknown without confusing them.