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12
DPLL with a trace: From SAT to knowledge compilation
 IJCAI05
, 2005
"... We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of dDNNF, FBDD, and OBDD, respectively. These languages are decreasingly s ..."
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Cited by 21 (2 self)
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We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of dDNNF, FBDD, and OBDD, respectively. These languages are decreasingly succinct, yet increasingly tractable, supporting such polynomialtime queries as model counting and equivalence testing. Our contribution is thus twofold. First, we provide a uniform framework, supported by empirical evaluations, for compiling knowledge into various languages of interest. Second, we show that given a particular variant of DPLL, by identifying the language membership of its traces, one gains a fundamental understanding of the intrinsic complexity and computational power of the search algorithm itself. As interesting examples, we unveil the “hidden power” of several recent model counters, point to one of their potential limitations, and identify a key limitation of DPLLbased procedures in general.
AND/OR multivalued decision diagrams (AOMDDs) for weighted graphical models
 In Proceedings of the Twenty Third Conference on Uncertainty in Artificial Intelligence (UAI’07
, 2007
"... Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical model ..."
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Cited by 11 (3 self)
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Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment MultiValued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR MultiValued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is searchbased, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inferencebased and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs. 1.
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 and to explicitly represent them in their most natural way. The resulting representation languages are analyzed according to their succinctness, supported queries, and supported transformations. The paper shows that most results from PDAGs, NNFs, and BDDs can be generalized to their corresponding multistate extension. This implies that the entire knowledge compilation map is extensible from propositional to multistate variables. 1
Compilation of queryrewriting problems into tractable fragments of propositional logic
 In AAAI
"... We consider the problem of rewriting a query efficiently using materialized views. In the context of information integration, this problem has received significant attention in the scope of emerging infrastructures such as WWW, Semantic Web, Grid, and P2P which require efficient algorithms. The prob ..."
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Cited by 8 (3 self)
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We consider the problem of rewriting a query efficiently using materialized views. In the context of information integration, this problem has received significant attention in the scope of emerging infrastructures such as WWW, Semantic Web, Grid, and P2P which require efficient algorithms. The problem is in general intractable, and the current algorithms do not scale well when the number of views or the size of the query grow. We show however that this problem can be encoded as a propositional theory in CNF such that its models are in correspondence with the rewritings of the query. The theory is then compiled into a normal form, that is called dDNNF and supports several operations like model counting and enumeration in polynomial time (in the size of the compiled theory), for computing the rewritings. Although this method is also intractable in the general case, it is not necessarily so in all cases. We have developed, along these lines and from offtheshelf propositional engines, novel algorithms for finding maximallycontained rewritings of the query given the set of accessible resources (views). The algorithms scale much better than the current stateoftheart algorithm, the MiniCon algorithm, over a large number of benchmarks and show in some cases improvements in performance of a couple ordersofmagnitude.
Fast dDNNF Compilation with sharpSAT
"... Knowledge compilation is a valuable tool for dealing with the computational intractability of propositional reasoning. In knowledge compilation, a representation in a source language is typically compiled into a target language in order to perform some reasoning task in polynomial time. One particul ..."
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Cited by 5 (2 self)
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Knowledge compilation is a valuable tool for dealing with the computational intractability of propositional reasoning. In knowledge compilation, a representation in a source language is typically compiled into a target language in order to perform some reasoning task in polynomial time. One particularly popular target language is Deterministic Decomposable Negation Normal Form (dDNNF). dDNNF supports efficient reasoning for tasks such as consistency checking and model counting, and as such it has proven a useful representation language for Bayesian inference, conformant planning, and diagnosis. In this paper, we exploit recent advances in #SAT solving in order to produce a new stateoftheart CNF → dDNNF compiler. We evaluate the properties and performance of our compiler relative to C2D, the de facto standard for compiling to dDNNF. Empirical results demonstrate that our compiler is generally one order of magnitude faster than C2D on typical benchmark problems while yielding a dDNNF representation of comparable size. 1
Heuristics for planning with penalties and rewards formulated in logic and computed through circuits
, 2008
"... ..."
The Language of Search
"... This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, an ..."
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Cited by 3 (0 self)
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This paper is concerned with a class of algorithms that perform exhaustive search on propositional knowledge bases. We show that each of these algorithms defines and generates a propositional language. Specifically, we show that the trace of a search can be interpreted as a combinational circuit, and a search algorithm then defines a propositional language consisting of circuits that are generated across all possible executions of the algorithm. In particular, we show that several versions of exhaustive DPLL search correspond to such wellknown languages as FBDD, OBDD, and a preciselydefined subset of dDNNF. By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various languages of interest, and a new methodology whereby the power and limitations of search algorithms can be understood by looking up the tractability and succinctness of the corresponding propositional languages. 1.
Mapping Conformant Planning into SAT through Compilation and Projection
"... Abstract. Conformant planning is a variation of classical AI planning where the initial state is partially known and actions can have nondeterministic effects. While a classical plan must achieve the goal from a given initial state using deterministic actions, a conformant plan must achieve the goal ..."
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Cited by 2 (1 self)
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Abstract. Conformant planning is a variation of classical AI planning where the initial state is partially known and actions can have nondeterministic effects. While a classical plan must achieve the goal from a given initial state using deterministic actions, a conformant plan must achieve the goal in the presence of uncertainty in the initial state and action effects. Conformant planning is computationally harder than classical planning, and unlike classical planning, cannot be reduced polynomially to SAT (unless P = NP). Current SAT approaches to conformant planning, such as those considered by Giunchiglia and colleagues, thus follow a generateandtest strategy: the models of the theory are generated one by one using a SAT solver (assuming a given planning horizon), and from each such model, a candidate conformant plan is extracted and tested for validity using another SAT call. This works well when the theory has few candidate plans and models, but otherwise is too inefficient. In this paper we propose a different use of a SAT engine for computing conformant plans where the existence of conformant plans and their extraction is carried out by means of a single SAT call over a transformed theory. This transformed theory is obtained by projecting the original theory over the action variables. This operation, while intractable, can be done efficiently provided that the original theory is compiled into DNNF (Darwiche 2000), a form akin to OBDDs (Bryant 1992). The experiments that are reported show that the resulting compileprojectsat planner is competitive with stateoftheart optimal conformant planners and improves upon a planner recently reported at ICAPS05. The techniques apply in direct fashion to the solution of QBFs of the form ∃x ∀y ∃z φ which are in correspondence to the problem of verifying the existence of conformant plans for a given horizon. 1
Complexity Results for Quantified Boolean Formulae Based on Complete Propositional Languages ∗ Sylvie CosteMarquis
, 2005
"... rue de l’Université — S.P. 16, ..."
Logical Compilation of Bayesian Networks with Discrete Variables
"... Abstract. This paper presents a new approach to inference in Bayesian networks. The principal idea is to encode the network by logical sentences and to compile the resulting encoding into an appropriate form. From there, all possible queries are answerable in linear time relative to the size of the ..."
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Cited by 1 (1 self)
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Abstract. This paper presents a new approach to inference in Bayesian networks. The principal idea is to encode the network by logical sentences and to compile the resulting encoding into an appropriate form. From there, all possible queries are answerable in linear time relative to the size of the logical form. Therefore, our approach is a potential solution for realtime applications of probabilistic inference with limited computational resources. The underlying idea is similar to both the differential and the weighted model counting approach to inference in Bayesian networks, but at the core of the proposed encoding we avoid the transformation from discrete to Boolean variables. This alternative encoding enables a more natural solution. 1