Abstract

Abstract. Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an off-line compilation phase and an online query-answering phase. In the off-line phase, the propositional theory is compiled into some target language, which is typically a tractable one. In the on-line phase, the compiled target is used to efficiently answer a (potentially) exponential number of queries. The main motivation behind knowledge compilation is to push as much of the computational overhead as possible into the offline phase, in order to amortize that overhead over all on-line queries. Another motivation behind compilation is to produce very simple on-line reasoning systems, which can be embedded costeffectively into primitive computational platforms, such as those found in consumer electronics. One of the key aspects of any compilation approach is the target language into which the propositional theory is compiled. Previous target languages included Horn theories, prime implicates/implicants and ordered binary decision diagrams (OBDDs). We propose in this paper a new target compilation language, known as decomposable negation normal form (DNNF), and present a number of its properties that make it of interest to the broad community. Specifically, we

Citations

2605	Graph-based algorithms for Boolean function manipulation - Bryant - 1986
837	Temporal constraint networks - Dechter, Meiri, et al. - 1991
792	Symbolic boolean manipulation with ordered binary decision diagrams - Bryant - 1992
765	A theory of diagnosis from first principles - Reiter - 1987
568	Diagnosing multiple faults - Kleer, Williams
320	Graph minors II: Algorithmic aspects of tree-width - Robertson, Seymour - 1986
291	A neutral netlist of 10 combinational benchmark circuits and a target translator - Brglez, Fujiwara - 1985
267	Complexity of finding embeddings in a k-tree - Arnborg, Corneil, et al. - 1987
224	On the complexity of VLSI implementations and graph representation of boolean functions with application to integer multiplication - BRYANT - 1991
183	Efficient algorithms for combinatorial problems on graphs with bounded decomposability - a survey - Arnborg - 1985
175	A linear time algorithm for finding treedecompositions of small treewidth - Bodlaender - 1996
171	Characterizing diagnoses and systems - Kleer, Mackworth, et al. - 1992
167	A tourist guide through treewidth - Bodlaender - 1993
134	Knowledge compilation and theory approximation - Selman, Kautz - 1996
130	Building Problem Solvers - Forbus, Kleer - 1993
109	Recursive conditioning - Darwiche - 2001
90	Directional resolution: the Davis–Putnam procedure, revisited, in - Dechter, Rish - 1994
89	A survey on knowledge compilation - Cadoli, Donini - 1998
64	F.: Forget it - Reiter, Lin - 1994
56	A reactive planner for a model-based executive - Williams, Nayak - 1997
53	Learning to reason - Khardon, Roth - 1997
51	Model-based diagnosis using structured system descriptions - Darwiche
45	Knowledge compilation using theory prime implicates - Marquis - 1995
43	Graph driven BDDs -- a new data structure for Boolean functions - Sieling, Wegener - 1995
42	On the tractable counting of theory models and its application to belief revision and truth maintenance. CoRR cs.AI/0003044 - Darwiche
35	Tractable databases: How to make propositional unit resolution complete through compilation - Val - 1994
30	A Symbolic Generalization of Probability Theory - Darwiche - 1992
30	Compiling Knowledge into Decomposable Negation Normal Form - Darwiche - 1999
25	A linear time algorithm for tree-decompositions of small treewidth - Bodlaender - 1996
23	Compiling devices: A structure-based approach - Darwiche - 1998
19	A theory of diagnosis from principles - Reiter - 1987
17	Complexity of embeddings in a k-tree - Arnborg, Corneil, et al. - 1987
17	Tractable cover compilations - Boufkhad, Grégoire, et al. - 1997
15	Sample method for minimization of obdds - Meinel, Slobodov'a - 1998
12	On some tractable classes in deduction and abduction - Val
11	Characterization and Recognition of Partial k-trees - Arnborg, Proskurowski - 1986
11	A very simple function that requires exponential-size read-once branching programs - Bollig, Wegener - 1998
10	Graph driven BDDs---a new data structure for Boolean functions - Sieling, Wegner - 1994
6	Boolean manipulation with free BDD's. First experimental results - Bern, Gergov, et al. - 1994
5	Compiling devices and processes - Kleer - 1990
5	A neutral netlist of 10 combinational benchmark circuits and a target translator in fortran - Beglez, Fujiwara - 1985
4	Model-based diagnosis under real-world constraints - Darwiche - 2000
3	An evaluation of structural paramters for probabilistic reasoning: Results on benchmark circuits - Fattah - 1996
2	Ecient analysis and manipulation of OBDDs can be extended to FBDDs - Gergov, Meinel - 1994
1	Boolean manipulation with free bdds: experimental results - Bern, Gergov, et al. - 1994
1	Decomposable Negation Normal Form 647 - GERGOV, MEINEL - 1994