1,700 research outputs found
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
The Connectivity of Boolean Satisfiability: Dichotomies for Formulas and Circuits
For Boolean satisfiability problems, the structure of the solution space is
characterized by the solution graph, where the vertices are the solutions, and
two solutions are connected iff they differ in exactly one variable. In 2006,
Gopalan et al. studied connectivity properties of the solution graph and
related complexity issues for CSPs, motivated mainly by research on
satisfiability algorithms and the satisfiability threshold. They proved
dichotomies for the diameter of connected components and for the complexity of
the st-connectivity question, and conjectured a trichotomy for the connectivity
question. Recently, we were able to establish the trichotomy [arXiv:1312.4524].
Here, we consider connectivity issues of satisfiability problems defined by
Boolean circuits and propositional formulas that use gates, resp. connectives,
from a fixed set of Boolean functions. We obtain dichotomies for the diameter
and the two connectivity problems: on one side, the diameter is linear in the
number of variables, and both problems are in P, while on the other side, the
diameter can be exponential, and the problems are PSPACE-complete. For
partially quantified formulas, we show an analogous dichotomy.Comment: 20 pages, several improvement
Evaluating QBF Solvers: Quantifier Alternations Matter
We present an experimental study of the effects of quantifier alternations on
the evaluation of quantified Boolean formula (QBF) solvers. The number of
quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is
directly related to the theoretical hardness of the respective QBF
satisfiability problem in the polynomial hierarchy. We show empirically that
the performance of solvers based on different solving paradigms substantially
varies depending on the numbers of alternations in PCNFs. In related
theoretical work, quantifier alternations have become the focus of
understanding the strengths and weaknesses of various QBF proof systems
implemented in solvers. Our results motivate the development of methods to
evaluate orthogonal solving paradigms by taking quantifier alternations into
account. This is necessary to showcase the broad range of existing QBF solving
paradigms for practical QBF applications. Moreover, we highlight the potential
of combining different approaches and QBF proof systems in solvers.Comment: preprint of a paper to be published at CP 2018, LNCS, Springer,
including appendi
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