Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Graph driven BDDs—a new data structure for Boolean functions
Theoretical Computer Science
A simple function that requires exponential size read-once branching programs
Information Processing Letters
A very simple function that requires exponential size read-once branching programs
Information Processing Letters
Symbolic manipulation of Boolean functions using a graphical representation
DAC '85 Proceedings of the 22nd ACM/IEEE Design Automation Conference
Equivalences Among Relational Expressions with the Union and Difference Operators
Journal of the ACM (JACM)
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Efficient Boolean Manipulation with OBDD's Can be Extended to FBDD's
IEEE Transactions on Computers
Optimal implementation of conjunctive queries in relational data bases
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
A survey on knowledge compilation
AI Communications
Management of probabilistic data: foundations and challenges
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The dichotomy of conjunctive queries on probabilistic structures
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient query evaluation on probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
Using OBDDs for Efficient Query Evaluation on Probabilistic Databases
SUM '08 Proceedings of the 2nd international conference on Scalable Uncertainty Management
Containment of conjunctive queries on annotated relations
Proceedings of the 12th International Conference on Database Theory
Journal of Artificial Intelligence Research
BDDs-design, analysis, complexity, and applications
Discrete Applied Mathematics
Provenance for database transformations
Proceedings of the 13th International Conference on Extending Database Technology
Computing query probability with incidence algebras
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Read-once functions and query evaluation in probabilistic databases
Proceedings of the VLDB Endowment
Relax, compensate and then recover
JSAI-isAI'10 Proceedings of the 2010 international conference on New Frontiers in Artificial Intelligence
Local structure and determinism in probabilistic databases
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
On the tractability of query compilation and bounded treewidth
Proceedings of the 15th International Conference on Database Theory
Probabilistic databases with MarkoViews
Proceedings of the VLDB Endowment
Dsharp: fast d-DNNF compilation with sharpSAT
Canadian AI'12 Proceedings of the 25th Canadian conference on Advances in Artificial Intelligence
The dichotomy of probabilistic inference for unions of conjunctive queries
Journal of the ACM (JACM)
A temporal-probabilistic database model for information extraction
Proceedings of the VLDB Endowment
Anytime approximation in probabilistic databases
The VLDB Journal — The International Journal on Very Large Data Bases
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The goal of Knowledge Compilation is to represent a Boolean expression in a format in which it can answer a range of online-queries in PTIME. The online-query of main interest to us is model counting, because of its application to query evaluation on probabilistic databases, but other online-queries can be supported as well such as testing for equivalence, testing for implication, etc. In this paper we study the following problem. Given a database query q, decide whether its lineage can be compiled efficiently into a given target language. We consider four target languages, of strictly increasing expressive power(when the size of compilation is constrained to be polynomial in the input size): Read-Once Boolean formulae, OBDD, FBDD and d-DNNF. For each target, we study the class of database queries that admit polynomial size representation: these queries can also be evaluated in PTIME over probabilistic databases. When queries are restricted to conjunctive queries without self-joins, it was known that these four classes collapse to the class of hierarchical queries, which is also the class of PTIME queries over probabilistic databases. Our main result in this paper is that, in the case of Unions of Conjunctive Queries (UCQ), these classes form a strict hierarchy. Thus, unlike conjunctive queries without self-joins, the expressive power of UCQ differs considerably w.r.t. these target compilation languages. Moreover, we give a complete characterization of the first two target languages, based on the query's syntax.