[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86243-en":3,"doc-seo-86243-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86243,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Enhancing Query Efficiency for d-DNNF Representations Through Preprocessing","This paper studies preprocessing methods that improve efficient access to models of propositional formulas in conjunctive normal form (CNF). Three core tasks are analyzed: uniform sampling, direct model access, and model enumeration. Results show many state-of-the-art preprocessors fail these tasks when they do not preserve formula equivalence. In contrast, preprocessing that preserves model counts can be used effectively when relevant preprocessing information is retained. Extensive experiments on multi-domain benchmarks confirm strong, robust performance gains for CNF compiled into d-DNNF.","arXiv :2607 . 1 1492v 1 [ cs .AI] 13 Jul 2026  \nEnhancing Query Efficiency for d-DNNF Representations Through Preprocessing  \nJean Marie Lagniez [0000−0002−6557−4115] and Emmanuel Lonca [0000−0002−9502−2821]  \nCRIL, U. Artois & CNRS, F-62300 Lens, France  \n{lagniez, [lonca}@cril.fr](lonca}@cril.fr)  \nAbstract. In this paper, we investigate preprocessing techniques aimed at improving the efficiency of accessing models of propositional formulas represented in conjunctive normal form (CNF) . We focus on three fundamental tasks: uniform sampling, direct model access, and model enumeration. Our analysis reveals that most state-of-the-art preprocessors, when they do not preserve formula equivalence, are generally unsuitable for these tasks. In contrast, we demonstrate that preprocessors which preserve model counts can be effectively leveraged, provided relevant preprocessing information is maintained. To validate our approach, we perform extensive experiments on a diverse suite of benchmarks from multiple domains. The experimental results show that our preprocessing methods are both efficient and robust, yielding significant performance improvements for model access queries when CNF formulas are compiled into d-DNNF representations.  \nKeywords: Preprocessing techniques · Uniform sampling · Direct access · Model enumeration · Decision-DNNF  \n1 Introduction  \nPropositional logic forms the backbone of a wide array of fields, including databases [1], automated planning [11], and explainable artificial intelligence [9], among others. When problems from these domains are encoded as propositional formulas, efficiently querying these formulas becomes essential for extracting meaningful insights and solving practical tasks. Crucial queries in this context include model counting, direct access, uniform sampling, and model enumeration. However, the computational complexity of these queries, often \\#P-complete, poses significant challenges, making the choice of suitable formula representations highly influential to overall performance. In this work, we focus specifically on formulas expressed in conjunctive normal form (CNF), the predominant representation in many practical settings due to its compatibility with modern SAT solvers and widespread use in real-world applications.  \nTo overcome the inherent computational difficulties associated with these queries on CNF formulas, preprocessing has emerged as a vital strategy. Preprocessing involves transforming a CNF formula into an equivalent (or, under certain relaxations, satisfiability-equivalent) CNF representation that is better suited for efficient query evaluation. Such transformations are valuable if they facilitate downstream tasks, even after accounting for the preprocessing cost itself. Indeed, preprocessing has proven effective  \n2 Lagniez and Lonca  \nacross a variety of reasoning tasks, such as SAT solving [3], model counting [22,29], and almost-uniform sampling [28], often yielding significant runtime improvements.  \nThis paper provides a comprehensive analysis of elementary preprocessing techniques, with a particular focus on their impact and suitability for direct access, uniform sampling, and model enumeration tasks. The techniques considered include vivification, occurrence reduction, backbone identification, variable elimination, blocked clause elimination, and the removal of implicitly and explicitly defined variables [22,19] . Notably, the first three techniques preserve full logical equivalence, making them broadly applicable regardless of the specific query. In contrast, variable elimination and blocked clause elimination only preserve satisfiability, limiting their utility for our target queries. Finally, under certain conditions, eliminating implicitly or explicitly defined variables (while preserving the model count) can enable more efficient solutions for direct access, uniform sampling, and model enumeration.  \nTo empirically evaluate the practical benefits of preproces","cbCaikC5ya7UlXxP","https://ap.wps.com/l/cbCaikC5ya7UlXxP","pdf",314925,2,1,16,"English","en",105,"# Introduction\n# Formal Preliminaries\n# Preprocessing Techniques and Applicability\n# Experimental Results\n# Conclusion","[{\"question\":\"Which tasks are used to evaluate preprocessing for CNF model access?\",\"answer\":\"The paper evaluates uniform sampling, direct model access, and model enumeration on CNF formulas compiled into d-DNNF representations.\"},{\"question\":\"Why can many preprocessors be unsuitable for these tasks?\",\"answer\":\"Most state-of-the-art preprocessors are unsuitable when they do not preserve formula equivalence, which breaks the required access properties for the target queries.\"},{\"question\":\"What property enables preprocessing to work well for model access in this setting?\",\"answer\":\"Preprocessors that preserve model counts can be leveraged effectively, provided the approach maintains the relevant preprocessing information needed to reconstruct answers on the original model 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