Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF

Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency sch...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of automated reasoning Ročník 63; číslo 3; s. 597 - 623
Hlavní autori: Beyersdorff, Olaf, Blinkhorn, Joshua, Chew, Leroy, Schmidt, Renate, Suda, Martin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.10.2019
Springer Nature B.V
Predmet:
Artificial Intelligence
Boolean algebra
Computer Science
Dependence
Mapping
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Reduction
Symbolic and Algebraic Manipulation
Quantified Boolean formulas
DQBF
F.2.2 Nonnumerical algorithms and problems
Dependency schemes
ISSN:0168-7433, 1573-0670, 1573-0670
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:Dependency quantified Boolean formulas (DQBF) and QBF dependency schemes have been treated separately in the literature, even though both treatments extend QBF by replacing the linear order of the quantifier prefix with a partial order. We propose to merge the two, by reinterpreting a dependency scheme as a mapping from QBF into DQBF. Our approach offers a fresh insight on the nature of soundness in proof systems for QBF with dependency schemes, in which a natural property called ‘full exhibition’ is central. We apply our approach to QBF proof systems from two distinct paradigms, termed ‘universal reduction’ and ‘universal expansion’. We show that full exhibition is sufficient (but not necessary) for soundness in universal reduction systems for QBF with dependency schemes, whereas for expansion systems the same property characterises soundness exactly. We prove our results by investigating DQBF proof systems, and then employing our reinterpretation of dependency schemes. Finally, we show that the reflexive resolution path dependency scheme is fully exhibited, thereby proving a conjecture of Slivovsky.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0168-7433
1573-0670
1573-0670
DOI:10.1007/s10817-018-9482-4