Conformant Planning as a Case Study of Incremental QBF Solving

Egly, Uwe; Kronegger, Martin; Lonsing, Florian; Pfandler, Andreas

doi:10.1007/978-3-319-13770-4_11

Cited by 17 publications

(14 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…QBFs extend propositional formulas by universal and existential quantifiers over Boolean variables [34] resulting in a decision problem that is PSPACE-complete. Applications from verification and synthesis [10,15,16,20,22,26], realizability checking [21], bounded model checking [18,52], and planning [19,44] motivate the quest for efficient QBF solvers (see [45] for a survey).…”

Section: Introductionmentioning

confidence: 99%

Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

Bloem

Braud-Santoni

Hadzic

et al. 2021

Form Methods Syst Des

Self Cite

View full text Add to dashboard Cite

In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over Boolean variables. Such approaches partially expand one type of variable (either existential or universal) for obtaining a propositional abstraction of the QBF. If this formula is false, the truth value of the QBF is decided, otherwise further refinement steps are necessary. Classically, expansion-based solvers process the given formula quantifier-block wise and use one SAT solver per quantifier block. In this paper, we present a novel algorithm for expansion-based QBF solving that deals with the whole quantifier prefix at once. Hence recursive applications of the expansion principle are avoided and only two incremental SAT solvers are required. While our algorithm is naturally based on the $$\forall $$ ∀ Exp+Res calculus that is the formal foundation of expansion-based solving, it is conceptually simpler than present recursive approaches. Experiments indicate that the performance of our simple approach is comparable with the state of the art of QBF solving, especially in combination with other solving techniques.

show abstract

Section: Introductionmentioning

confidence: 99%

Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

Bloem

Braud-Santoni

Hadzic

et al. 2021

Form Methods Syst Des

Self Cite

View full text Add to dashboard Cite

show abstract

“…The algorithmic success story of solving has not stopped at SAT, but is currently extending to even more computationally complex problems such as quantified Boolean formulas (QBF), which is complete, and dependency QBFs (DQBF), which is even complete [ 1 ]. While quantification does not increase expressivity, (D)QBFs can encode many problems far more succinctly, including application domains such as automated planning [ 18 , 22 ], verification [ 6 , 41 ], synthesis [ 24 , 40 ] and ontologies [ 37 ].…”

Section: Introductionmentioning

confidence: 99%

Building Strategies into QBF Proofs

2020

View full text Add to dashboard Cite

Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving.

show abstract

“…These build on the success of SAT solving [36], but also incorporate new ideas genuine to the QBF domain, such as expansion solving [21] and dependency schemes [32]. Due to its PSPACE completeness, QBF solving is relevant to many application domains that cannot be efficiently encoded into SAT [17,23,26]. On the theoretical side, there is a substantial body of QBF proof complexity results (e.g.…”

Section: Introductionmentioning

confidence: 99%

Strong (D)QBF Dependency Schemes via Tautology-Free Resolution Paths

Beyersdorff

Blinkhorn

Peitl

2020

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We suggest a general framework to study dependency schemes for dependency quantified Boolean formulas (DQBF). As our main contribution, we exhibit a new tautology-free DQBF dependency scheme that generalises the reflexive resolution path dependency scheme. We establish soundness of the tautology-free scheme, implying that it can be used in any DQBF proof system. We further explore the power of DQBF resolution systems parameterised by dependency schemes and show that our new scheme results in exponentially shorter proofs in comparison to the reflexive resolution path dependency scheme when used in the expansion DQBF system ∀Exp+Res.On QBFs, we demonstrate that our new scheme is exponentially stronger than the reflexive resolution path dependency scheme when used in Q-resolution, thus resulting in the strongest QBF dependency scheme known to date.

show abstract

Conformant Planning as a Case Study of Incremental QBF Solving

Cited by 17 publications

References 33 publications

Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

Two SAT solvers for solving quantified Boolean formulas with an arbitrary number of quantifier alternations

Building Strategies into QBF Proofs

Strong (D)QBF Dependency Schemes via Tautology-Free Resolution Paths

Contact Info

Product

Resources

About