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About 1,832 papers for “Boolean formulas”

Encoding Nested Boolean Functions as Quantified Boolean Formulas

Uwe Bubeck, Hans Kleine Büning · Journal on Satisfiability Boolean Modeling and Computation · 2012

In this paper, we consider the problem of compactly representing nested instantiations of propositional subformulas with different arguments as quantified Boolean formulas (QBF). We develop a generic QBF encoding pattern which combines and generalize

Cited by 4Open access

Boolean Formulas and Frequent Sets

Jouni Seppnen And, Heikki Mannila · 2005

We consider the problem of how one can estimate the support of Boolean queries given a collection of frequent itemsets. We describe an algorithm that truncates the inclusion-exclusion sum to include only the frequencies of known itemsets, give a bound for its performance on disjunctions of attributes that is smaller than the previously known bound, and show that this bound is in fact achievable. We also show how to generalize the algorithm to approximate arbitrary Boolean queries. 1

Cited by 0

Chapter 31. Quantified Boolean Formulas

Olaf Beyersdorff, Mikoláš Janota, Florian Lonsing et al. · Frontiers in artificial intelligence and applications · 2021

Solvers for quantified Boolean formulas (QBF) have become powerful tools for tackling hard computational problems from various application domains, even beyond the scope of SAT. This chapter gives a description of the main algorithmic paradigms for QBF solving, including quantified conflict driven clause learning (QCDCL), expansion-based solving, dependency schemes, and QBF preprocessing. Particular emphasis is laid on the connections of these solving approaches to QBF proof systems: Q-Resolution and its variants in the case of QCDCL, expansion QBF resolution calculi for expansion-based solving, and QRAT for preprocessing. The chapter also surveys the relations between the various QBF proof systems and results on their proof complexity, thereby shedding light on the diverse performance characteristics of different solving approaches that are observed in practice.

Cited by 22

Theory of Quantified Boolean Formulas

Kleine B uuml ning Hans, Bubeck Uwe · Frontiers in artificial intelligence and applications · 2009

Quantified Boolean formulas (QBF) are a generalization of propositional formulas by allowing universal and existential quantifiers over variables. This enhancement makes QBF a concise and natural modeling language in which problems from many areas, such as planning, scheduling or verification, can often be encoded in a more compact way than with propositional formulas.

Cited by 64

Proof Complexity for Quantified Boolean Formulas

Judith Clymo · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · 2020

Quantified Boolean formulas (QBF) extend the propositional satisfiability problem by allowing variables to be universally as well as existentially quantified. Deciding whether a QBF is true or false is PSPACE-complete and a wide range of mathematical and industrial problems can be expressed as QBFs. QBF proof complexity is the theoretical analysis of algorithmic techniques for solving QBFs.
\nWe make a detailed comparison of the proof systems Q-Res, QU-Res, and ∀Exp + Res which extend propositional Resolution with different rules for reasoning about universally quantified variables. We give new simulation and separation results between these proof systems under two natural restrictions, when the proofs are tree-like, and when the QBFs have bounded quantifier complexity.
\nWe consider a strong QBF proof system, QRAT, proposed as a universal proof checking format. We show that, unless P = PSPACE, QRAT does not admit strategy extraction. This is proved by constructing a family of QBFs that have short QRAT proofs but whose strategies are hard to compute in general. We also explore why strategy extraction fails for QRAT, including presenting a restricted version of QRAT which does admit strategy extraction.
\nWe study two results from propositional proof complexity and their analogues in QBF proof complexity, showing in both cases how the additional complexity of QBF solving compared to refuting propositional formulas causes these results to fail in the QBF setting.

Cited by 2Open access

Message passing for quantified Boolean formulas

Zhang, Pan, Ramezanpour, Abolfazl, Zdeborová, Lenka et al. · arXiv (Cornell University) · 2012

We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics gives robust exponential efficiency gain with respect to the state-of-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this our study sheds light on using message passing in small systems and as subroutines in complete solvers.

Cited by 0Open access

Fault diagnosis using quantified boolean formulas

Hratch Mangassarian, Andreas Veneris, Marco Benedetti · 2007

Abstract — Automatic debugging of sequential circuits has been considered a practically intractable task due to the excessive memory and run-time requirements associated with tackling industrial-size problems. This paper proposes a novel Quantified Boolean Formula (QBF) based approach for fault diagnosis in sequential circuits. A performance-driven succinct QBF encoding of the problem, coupled with the tremendous present-day advances in QBF solvers make this strategy a successful one. Extensive experiments on industrial circuits confirm the memory advantage and demonstrate the outstanding performance of the proposed framework. I.

Cited by 2

Function Problems for Quantified Boolean Formulas

S. Coste-marquis, H. Fargier, J. Lang et al. · 2003

The practical use of Quantified Boolean Formulas (QBFs) often calls for more than solving the evaluation problem QBF. For this reason we investigate the corresponding function problem FQBF. We define expected outputs of FQBF instances as solution policies. We focus on the representation of policies, considering QBFs of the form ∀X ∃Y Φ. Because the explicit representation of policies for such QBFs can be of exponential size, descriptions as compact as possible must be looked for. To address this issue, two approaches based on the decomposition and the compilation of Φ are presented.

Cited by 0