Boolean Quantifier Elimination for Automotive Configuration – A Case Study

Zengler, Christoph; Küchlin, Wolfgang

doi:10.1007/978-3-642-41010-9_4

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…A counting characterization of diagnoses is presented in [18]. Propositional model counting finds further applications in product configuration [32,17] and planning [1,31].…”

Section: Introductionmentioning

confidence: 99%

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

Möhle¹,

Biere²

EPiC Series in Computing

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In propositional model counting, also named #SAT, the search space needs to be explored exhaustively, in contrast to SAT, where the task is to determine whether a propositional formula is satisfiable. While state-of-the-art SAT solvers are based on non- chronological backtracking, it has also been shown that backtracking chronologically does not significantly degrade solver performance. Hence investigating the combination of chronological backtracking with conflict-driven clause learning (CDCL) for #SAT seems evident. We present a calculus for #SAT combining chronological backtracking with CDCL and provide a formal proof of its correctness.

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“…A counting characterization of diagnoses is presented in [18]. Propositional model counting finds further applications in product configuration [32,17] and planning [1,31].…”

Section: Introductionmentioning

confidence: 99%

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

Möhle¹,

Biere²

EPiC Series in Computing

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“…For completeness, we mention other languages, which are restricted variants of d-DNNF circuits, such as decision-DNNF circuits (Huang and Darwiche 2007), SDDs (Darwiche 2011), and OB-DDs (Bryant 1986). DNNF circuits have many applications, including diagnosis (Huang and Darwiche 2005;Siddiqi and Huang 2007;Siddiqi 2011), configuration (Voronov, Åkesson, and Ekstedt 2011;Zengler and Küchlin 2013), MaxSAT (Pipatsrisawat and Darwiche 2007;Ramírez and Geffner 2007), and planning (Bonet and Geffner 2006).…”

Section: Introductionmentioning

confidence: 99%

A Compiler for Weak Decomposable Negation Normal Form

Illner,

Kučera

2024

AAAI

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This paper integrates weak decomposable negation normal form (wDNNF) circuits, introduced by Akshay et al. in 2018, into the knowledge compilation map. This circuit type generalises decomposable negation normal form (DNNF) circuits in such a way that they allow a restricted form of sharing variables among the inputs of a conjunction node. We show that wDNNF circuits have the same properties as DNNF circuits regarding the queries and transformations presented in the knowledge compilation map, whilst being strictly more succinct than DNNF circuits (that is, they can represent Boolean functions compactly). We also present and evaluate a knowledge compiler, called Bella, for converting CNF formulae into wDNNF circuits. Our experiments demonstrate that wDNNF circuits are suitable for configuration instances.

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“…We say that we existentially quantify the formula over the irrelevant variables Y and write ∃Y [ F (X, Y ) ], where F (X, Y ) is a formula over variables X and Y such that X ∩ Y = ∅. Projected model enumeration occurs in automotive configuration [34], existential quantifier elimination [4], image computation [9,10], predicate abstraction [13], and bounded model checking [31].…”

Section: Introductionmentioning

confidence: 99%

Four Flavors of Entailment

Möhle

Sebastiani

Biere

2020

Theory and Applications of Satisfiability Testing – SAT 2020

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We present a novel approach for enumerating partial models of a propositional formula, inspired by how theory solvers and the SAT solver interact in lazy SMT. Using various forms of dual reasoning allows our CDCL-based algorithm to enumerate partial models with no need for exploring and shrinking full models. Our focus is on model enumeration without repetition, with potential applications in weighted model counting and weighted model integration for probabilistic inference over Boolean and hybrid domains. Chronological backtracking renders the use of blocking clauses obsolete. We provide a formalization and examples. We further discuss important design choices for a future implementation related to the strength of dual reasoning, including unit propagation, using SAT or QBF oracles.

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Boolean Quantifier Elimination for Automotive Configuration – A Case Study

Cited by 9 publications

References 15 publications

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

A Compiler for Weak Decomposable Negation Normal Form

Four Flavors of Entailment

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