Game-SAT: A Preliminary Report

Game-SAT is a 2-player version of SAT where two players (MAX and MIN) play on a SAT instance by alternatively selecting a variable and assigning it a value true or false. MAX tries to make the formula true, while MIN tries to make it false. The Game-SAT problem is to determine the winner of a SAT instance under the rules above, assuming the perfect play by both players. The Game-SAT problem, originally derived from an application in adversarial planning, is PSPACE-complete. The problem is similar to QBF, but differs by the property of free variable selection, compared to QBF with its fixed variable ordering. We have developed a Game-SAT solver, Gasaso, that uses a combination of standard game tree search techniques, search methods that are well known in the SAT community, and specialized pruning techniques. We show empirically how the solver performs in this new domain, and give evidence for the existence of phase transitions in this problem.