Never Trust Your Solver: Certification for SAT and QBF.

Many problems for formal verification and artificial intelligence rely on advanced reasoning technologies in the background, often in the form of SAT or QBF solvers. Such solvers are sophisticated and highly tuned pieces of software, often too complex to be verified themselves. Now the question arises how one can one be sure that the result of such a solver is correct, especially when its result is critical for proving the correctness of another system. If a SAT solver, a tool for deciding a propositional formula, returns satisfiable, then it also returns a model which is easy to check. If the answer is unsatisfiable, the situation is more complicated. And so it is for true and false quantified Boolean formulas (QBFs), which extend propositional logic by quantifiers over the Boolean variables. To increase the trust in a solving result, modern solvers are expected to produce certificates that can independently and efficiently be checked. In this paper, we give an overview of the state of the art on validating the results of SAT and QBF solvers based on certification.