A Knowledge Compilation Map

Darwiche, Adnan; Marquis, Pierre

doi:10.1613/jair.989

Cited by 558 publications

(817 citation statements)

References 26 publications

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“…Various forms of tractable structures have been suggested as target compilation languages, including automata [1], binary decision diagrams [2], and/or decision diagrams [3], and deterministic decomposable negation normal form (d-DNNF) [4].…”

Section: Introductionmentioning

confidence: 99%

Approximate Compilation of Constraints into Multivalued Decision Diagrams

Hadžić¹,

Hooker

O’Sullivan³

et al. 2008

Lecture Notes in Computer Science

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Abstract.We present an incremental refinement algorithm for approximate compilation of constraint satisfaction models into multivalued decision diagrams (MDDs). The algorithm uses a vertex splitting operation that relies on detection of equivalent paths in the MDD. Although the algorithm is quite general, it can be adapted to exploit constraint structure by specializing the path equivalence test to particular constraints. We show how to modify the algorithm in a principled way to obtain an approximate MDD when the exact MDD is too large for practical purposes. This is done by replacing the equivalence test with a constraint-specific measure of distance. We demonstrate the value of the approach for approximate and exact MDD compilation and evaluate its benefits in one of the main MDD application domains, interactive configuration.

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Section: Introductionmentioning

confidence: 99%

Approximate Compilation of Constraints into Multivalued Decision Diagrams

Hadžić¹,

Hooker

O’Sullivan³

et al. 2008

Lecture Notes in Computer Science

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“…In this paper we explore another such problem, and show that DPLL, coupled with appropriate caching, can be the basis for an efficient program that compiles propositional theories into Ordered Binary Decision Diagrams (OBDDs) [5]. Once theories are expressed as OBDDs, many important queries can be answered in constant or polynomial time, including satisfiability, equivalence, model counting, model enumeration, and clausal entailment [5,6].…”

Section: Introductionmentioning

confidence: 99%

Using DPLL for Efficient OBDD Construction

Huang

Darwiche

2005

Lecture Notes in Computer Science

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Abstract. The DPLL procedure has found great success in SAT, where search terminates on the first solution discovered. We show that this procedure is equally promising in a problem where exhaustive search is used, given that it is augmented with appropriate caching. Specifically, we propose two DPLL-based algorithms that construct OBDDs for CNF formulas. These algorithms have a worst-case complexity that is linear in the number of variables and size of the CNF, and exponential only in the cutwidth or pathwidth of the variable ordering. We show how modern SAT techniques can be harnessed by implementing the algorithms on top of an existing SAT solver. We discuss the advantage of this new construction method over the traditional approach, where OBDDs for subsets of the CNF formula are built and conjoined. Our experiments indicate that on many CNF benchmarks, the new method runs orders of magnitude faster than a comparable implementation of the traditional method.

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“…The key operation that is intractable is the projection. It is well known however that projection, like many other intractable boolean transformations, can be performed in linear time provided that the theory is in a suitable compiled form [20]. Of course, the compilation itself may run in exponential time and space, yet this will not be necessarily so on average.…”

Section: Conformant Planning and Modelsmentioning

confidence: 99%

“…d-DNNFs support a rich set of polynomial time operations and queries; in particular projection and model counting, that are intractable over CNFs, become linear operations over d-DNNFs. OBDDs are a special, less succint class of d-DNNFs; in fact, there are OBDDs that are exponentially larger than their equivalent d-DNNFs but not the other way around [24]. For both languages, OBDDs and d-DNNFs, there are public libraries that support compilation from CNF, along with a variety of queries and transformations.…”

Section: Conformant Planning and Modelsmentioning

confidence: 99%

Mapping Conformant Planning into SAT Through Compilation and Projection

Palacios

Geffner

2006

Current Topics in Artificial Intelligence

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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 generate-and-test 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 compile-project-sat planner is competitive with state-of-the-art optimal conformant planners and improves upon a planner recently reported at ICAPS-05. 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.

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A Knowledge Compilation Map

Cited by 558 publications

References 26 publications

Approximate Compilation of Constraints into Multivalued Decision Diagrams

Approximate Compilation of Constraints into Multivalued Decision Diagrams

Using DPLL for Efficient OBDD Construction

Mapping Conformant Planning into SAT Through Compilation and Projection

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