A Duality-Aware Calculus for Quantified Boolean Formulas

Abstract

Learning and backjumping are essential features in search-based decision procedures for Quantified Boolean Formulas (QBF). To obtain a better understanding of such procedures, we present a formal framework, which allows to simultaneously reason on prenex conjunctive and disjunctive normal form. It captures both satisfying and falsifying search states in a symmetric way. This symmetry simplifies the framework and offers potential for further variants.

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

“…A totally different approach, inspired by [13,10], was presented in [3,20]. It is dual, i.e., it takes as input a formula together with its negation.…”

Understanding and Extending Incremental Determinization for 2QBF

“…The approaches differ in that QCDCL does not reason about functions, but only about values of variables. Fazekas et al have formalized QCDCL as inference rules [16].…”

“…Related work. This work is written in the tradition of works such as the Model Evolution Calculus [13], AbstractDPLL [14], MCSAT [15], and recent calculi for QBF [16], which present search algorithms as inference rules to enable the study and extension of these algorithms. ID and the inference rules presented in this paper can be seen as an instantiation of the more general frameworks, such as MCSAT [15] or Abstract Conflict Driven Learning [17].…”