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Compiling constraint networks into AND/OR multivalued decision diagrams (AOMDDs)
 IN PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING (CP’06
, 2006
"... Inspired by AND/OR search spaces for graphical models recently introduced, we propose to augment Ordered Decision Diagrams with AND nodes, in order to capture function decomposition structure. This yields AND/OR multivalued decision diagram (AOMDD) which compiles a constraint network into a canonic ..."
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Cited by 19 (4 self)
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. The algorithm uses the APPLY operator which combines two AOMDDs by a given operation. This guarantees the complexity upper bound for the compilation time and the size of the AOMDD to be exponential in the treewidth of the constraint graph, rather than pathwidth as is known for ordered binary decision diagrams
On the use of partially ordered decision graphs in knowledge compilation and quantified Boolean formulae
 In Proc. of AAAI’06
, 2006
"... Decomposable Negation Normal Form formulae (DNNFs) form an interesting propositional fragment, both for efficiency and succinctness reasons. A famous subclass of the DNNF fragment is the OBDD fragment which offers many polytime queries and transformations, including quantifier eliminations (under so ..."
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Cited by 8 (4 self)
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“parallelization property”. This is why we suggest to go a step further, from (sequentially) ordered decision diagrams to (partially) ordered, decomposable decision graphs, in which any decomposable AND node is allowed, and not only assignment ones. We show that, like the OBDD fragment, such a new class offers
On the Role of Canonicity in Knowledge Compilation
"... Knowledge compilation is a powerful reasoning paradigm with many applications across AI and computer science more broadly. We consider the problem of bottomup compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boole ..."
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Cited by 2 (2 self)
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guage of Sentential Decision Diagrams (SDDs): while a polytime Apply function exists for SDDs, it was unknown whether such a function exists for the important subset of compressed SDDs which are canonical. We resolve this open question in this paper and consider some of its theoretical and practical implications
AND/OR multivalued decision diagrams for constraint networks
 IN: PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING
, 2007
"... The paper is an overview of a recently developed compilation data structure for graphical models, with specific application to constraint networks. The AND/OR MultiValued Decision Diagram (AOMDD) augments well known decision diagrams (OBDDs, MDDs) with AND nodes, in order to capture function decomp ..."
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Cited by 2 (0 self)
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The paper is an overview of a recently developed compilation data structure for graphical models, with specific application to constraint networks. The AND/OR MultiValued Decision Diagram (AOMDD) augments well known decision diagrams (OBDDs, MDDs) with AND nodes, in order to capture function
Constraint and Variable Ordering Heuristics for Compiling Configuration Problems
"... To facilitate interactive design, the solutions to configuration problems can be compiled into a decision diagram. We develop three heuristics for reducing the time and space required to do this. These heuristics are based on the distinctive clustered and hierarchical structure of the constraint gra ..."
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Cited by 9 (1 self)
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To facilitate interactive design, the solutions to configuration problems can be compiled into a decision diagram. We develop three heuristics for reducing the time and space required to do this. These heuristics are based on the distinctive clustered and hierarchical structure of the constraint
AND/OR MultiValued Decision Diagrams forConstraint Optimization
"... Abstract. We propose a new top down searchbased algorithm for compilingAND/OR MultiValued Decision Diagrams (AOMDDs), as representations of the optimal set of solutions for constraint optimization problems. The approach isbased on AND/OR search spaces for graphical models, stateoftheart AND/OR ..."
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Abstract. We propose a new top down searchbased algorithm for compilingAND/OR MultiValued Decision Diagrams (AOMDDs), as representations of the optimal set of solutions for constraint optimization problems. The approach isbased on AND/OR search spaces for graphical models, stateoftheart AND
On the Role of Canonicity in Bottomup Knowledge Compilation
"... Abstract We consider the problem of bottomup compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain ..."
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for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNF), its existence for certain languages remains unknown. Among the latter is the recently introduced language of Sentential Decision Diagrams (SDDs), for which a polytime Apply function exists for unreduced SDDs, but remains unknown
Multistate Directed Acyclic Graphs
 In Proc. Canadian AI
, 2007
"... Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and ..."
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Cited by 8 (3 self)
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Abstract. This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states
Automated Deduction with Shannon Graphs
 Journal of Logic and Computation. In
, 1995
"... Binary Decision Diagrams (BDDs) are a wellknown tool for representing Boolean functions. We show how BDDs can be extended to full firstorder logic by integrating means for representing quantifiers. The resulting structures are called Shannon graphs. A calculus based on these Shannon graphs is set ..."
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Cited by 4 (0 self)
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Binary Decision Diagrams (BDDs) are a wellknown tool for representing Boolean functions. We show how BDDs can be extended to full firstorder logic by integrating means for representing quantifiers. The resulting structures are called Shannon graphs. A calculus based on these Shannon graphs is set
Towards Firstorder Deduction Based on Shannon Graphs
, 1992
"... We present a new approach to Automated Deduction based on the concept of Shannon graphs, which are also known as Binary Decision Diagrams (BDDs). A Skolemized formula is first transformed into a Shannon graph, then the latter is compiled into a set of Horn clauses. These can finally be run as a P ..."
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We present a new approach to Automated Deduction based on the concept of Shannon graphs, which are also known as Binary Decision Diagrams (BDDs). A Skolemized formula is first transformed into a Shannon graph, then the latter is compiled into a set of Horn clauses. These can finally be run as a
Results 1  10
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35