SAT Solvers

There is a trivial algorithm for satisfiability checking: for each possible interpretation, check whether the conjunction of clauses is satisfied. The problem is that this is O(2ⁿ) when there are n literals.

However, there are some efficient algorithms:

• The Davis-Putnam or DPLL algorithm uses heuristics for early termination (determining the value from a partially specified model), pure symbols (those that have the same sign in all clauses) and unit clauses (those with a single literal).

  The CHAFF inplementation of DPLL solves hardware verification problems with a million variables.

• The WalkSAT algorithm uses a combination of hill climbing (selecting a literal assignment that makes the most clauses true) and random steps.