What are QBF? Quantified Boolean formulas (QBF) are formulas of propositional logic + quantifiers Examples: (x _: y)^(:x _ ) (propositional logic) 9 x8y( _:y)^(:x _y) Is there a value for x such that for all values of y the formula is true? 8y9 x( _:y)^(:x _y) For all values of y, is there a value for x such that the formula is true? 2

In computational complexity theory, the quantified Boolean formula problem (QBF) is a generalization of the Boolean satisfiability problem in which both existential quantifiers and universal quantifiers can be applied to each variable. Put another way, it asks whether a quantified sentential form over a set of Boolean variables is true or false ...

QSAT is the prototypical problem for PSPACE. Given an input-output specification, does there exists a circuit that satisfies the input-output specification. Many games, such as Go and Reversi, can be naturally expressed as a QBF problem. i and column j at his kth turn. Variables ci;k, dj;k are used for the universal player.

This tutorial will describe how this is done in the present-day QBF solvers, model counters, and solution samplers. It will also discuss some interesting issues that arise when extending SAT-based techniques to these harder problems.

Apr 27, 2021 · In this talk, we review two successful solving paradigms of orthogonal strength and their formal characterizations in terms of proof systems: Search-based QBF solving is based on Q-Resolution and expansion-based QBF solving is founded on the forall-Exp-Res proof system.

QBF is the problem of deciding the satisfiability of quantified boolean formulae in which variables can be either universally or existentially quantified. QBF generalizes SAT (SAT is QBF under the restriction all variables are exis-tential) and is in practice much harder to solve than SAT.

In this work, we overview two main 2QBF challenges in terms of solving and certification. We contribute several improvements to existing solving approaches and study how the corre-sponding approaches affect certification.

We employ two basic strategies in our work. One is to break the QBF into many small subformulas, and use dynamic progr. mming to solve the subformulas efficiently. The second is to search over all possible satisfying .

We present a novel approach to solving Quantified Boolean Formulas (QBF) that combines a search-based QBF solver with machine learning techniques. We show how classifica-tion methods can be used to predict run-times and to choose optimal heuristics both within a portfolio-based, and within a dynamic, online approach.

In this paper we analyze QBF from a theoretical perspective and are therefore interested in obtaining unconditionally improved algorithms.