A SAT-based solver for Q-ALL SAT

Abstract

Although the satisfiability problem (SAT) is NP-complete, state-of-the-art solvers for SAT can solve instances that are considered to be very hard. Emerging applications demand to solve even more complex problems residing at the second or higher levels of the polynomial hierarchy. We identify such a problem, called Q-ALL SAT, that arises in a variety of applications. We have designed a solution algorithm for Q-ALL SAT that employs a SAT solver and thus exploits the recent advances of SAT solvers. In addition, a heuristic is applied to reduce the number of instances that are to be solved by the SAT solver. A learning scheme improves the performance of that heuristic. Test results of a first implementation of the proposed algorithm confirm that this is a very promising approach.

Abstraction-Based Algorithm for 2QBF

“…However, this is infeasible since the formula grows exponentially. We continue by observing that the question whether a certain value vector is a solution can be formulated as a Boolean satisfiability question 3 .…”

“…Mneimneh and Sakallah compute the vertex eccentricity of a transition system (also known as the diameter) [25]. Browning and Remshagen tackle the validity of Q-ALL SAT [3]. Besides the fact that the algorithms presented in these articles are specialized to subsets of 2QBF, there is also an important difference in the refinement they use.…”

Solving QBF with Counterexample Guided Refinement

“…Special cases of QBF, with limited number of quantifiers, have been targeted by CEGAR: computing vertex eccentricity [22], nonmonotonic reasoning [6,16], two-level quantification [17]. Table 2.…”