An Exhaustive DPLL Algorithm for Model Counting

Öztok, Umut; Darwiche, Adnan

doi:10.1613/jair.1.11201

Cited by 9 publications

(9 citation statements)

References 17 publications

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“…Tractable Boolean circuits are normally compiled from Boolean formulas that represent logical knowledge or constraints. This is done using systems known as knowledge compilers, such as D4 [68], 2 [38], CUDD, -2 [79,80], DSHARP [76] and the SDD library [23]. 17 Knowledge compilers can be categorized as top-down or bottom-up.…”

Section: Further Extensionsmentioning

confidence: 99%

“…17 Knowledge compilers can be categorized as top-down or bottom-up. Topdown compilers are based on keeping a trace of the exhaustive DPLL algorithm [61] and they generally incorporate advanced SAT techniques [93,80]. These compilers normally operate on Boolean formulas in conjunctive normal form, tend to have better space complexity, and include D4, 2 and DSHARP which yield Decision-DNNFs, and -2 which yields SDDs.…”

Section: Further Extensionsmentioning

confidence: 99%

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Tractable Boolean and Arithmetic Circuits

Darwiche¹

2022

Preprint

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Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as "compiled objects," meant to facilitate logical and probabilistic reasoning, as they permit various types of inference to be performed in linear-time and a feed-forward fashion like neural networks. In more recent years, the role of tractable circuits has significantly expanded as they became a computational and semantical backbone for some approaches that aim to integrate knowledge, reasoning and learning. In this article, we review the foundations of tractable circuits and some associated milestones, while focusing on their core properties and techniques that make them particularly useful for the broad aims of neuro-symbolic AI.

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Section: Further Extensionsmentioning

confidence: 99%

Section: Further Extensionsmentioning

confidence: 99%

Tractable Boolean and Arithmetic Circuits

Darwiche¹

2022

Preprint

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“…The compilation of Boolean formula into tractable NNF circuits is done by systems known as knowledge compilers. Examples include c2d 9 [26], cudd 10 , mini-c2d 11 [62,63], d4 12 [46], dsharp 13 [56] and the sdd library [12]. 14 See also http://beyondnp.org/pages/ solvers/knowledge-compilers/.…”

Section: Tractable Circuitsmentioning

confidence: 99%

“…Some of the popular or traditional model counters are c2d[26], mini-c2d[63], d4[46], cache[73], sharp-sat[88], sdd[12] and dsharp[56]. Many of these systems can also compute weighted model counts.…”

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confidence: 99%

Three Modern Roles for Logic in AI

Darwiche

2020

Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems. CCS CONCEPTS • Computing methodologies → Learning in probabilistic graphical models; Logical and relational learning; • Theory of computation → Automated reasoning; Complexity classes; Problems, reductions and completeness.

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“…We experimented with bottom up (TheSDDPackage) as well as top down (MiniC2D) compilation strategies for SDDs, predefined total variable ordering against dynamic ordering for OBDDs (CUDD) and different decomposition techniques for d-DNNFs (C2D, Dsharp and D4). Notably, target language for MiniC2D is decision-SDD and CUDD with predefined total variable order is OBDD > [30,14], which are less succinct than SDD and OBDD respectively. We state our representative observations for 3-CNF here.…”

Section: Effect Of Different Toolsmentioning

confidence: 99%

Phase Transition Behavior in Knowledge Compilation

Gupta¹,

Roy²,

Meel³

2020

Preprint

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The study of phase transition behaviour in SAT has led to deeper understanding and algorithmic improvements of modern SAT solvers. Motivated by these prior studies of phase transitions in SAT, we seek to study the behaviour of size and compile-time behaviour for random k-CNF formulas in the context of knowledge compilation. We perform a rigorous empirical study and analysis of the size and runtime behavior for different knowledge compilation forms (and their corresponding compilation algorithms): d-DNNFs, SDDs and OBDDs across multiple tools and compilation algorithms. We employ instances generated from the random k-CNF model with varying generation parameters to empirically reason about the expected and median behavior of size and compilation-time for these languages. Our work is similar in spirit to the early work in CSP community on phase transition behavior in SAT/CSP. In a similar spirit, we identify the interesting behavior with respect to different parameters: clause density and solution density, a novel control parameter that we identify for the study of phase transition behavior in the context of knowledge compilation. Furthermore, we summarize our empirical study in terms of two concrete conjectures; a rigorous study of these conjectures will possibly require new theoretical tools.

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An Exhaustive DPLL Algorithm for Model Counting

Cited by 9 publications

References 17 publications

Tractable Boolean and Arithmetic Circuits

Tractable Boolean and Arithmetic Circuits

Three Modern Roles for Logic in AI

Phase Transition Behavior in Knowledge Compilation

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