Decomposable negation normal form
Journal of the ACM (JACM)
The Tree-Width of Clique-Width Bounded Graphs Without Kn, n
WG '00 Proceedings of the 26th International Workshop on Graph-Theoretic Concepts in Computer Science
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
Rank-width is less than or equal to branch-width
Journal of Graph Theory
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Journal of Artificial Intelligence Research
SIAM Journal on Discrete Mathematics
Reasoning in Argumentation Frameworks of Bounded Clique-Width
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Treewidth in verification: local vs. global
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
On the tractability of query compilation and bounded treewidth
Proceedings of the 15th International Conference on Database Theory
SDD: a new canonical representation of propositional knowledge bases
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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In this paper we study the role of cliquewidth in succinct representation of Boolean functions. Our main statement is the following: Let Z be a Boolean circuit having cliquewidth k. Then there is another circuit Z* computing the same function as Z having treewidth at most 18k+2 and which has at most 4|Z| gates where |Z| is the number of gates of Z. In this sense, cliquewidth is not more 'powerful' than treewidth for the purpose of representation of Boolean functions. We believe this is quite a surprising fact because it contrasts the situation with graphs where an upper bound on the treewidth implies an upper bound on the cliquewidth but not vice versa. We demonstrate the usefulness of the new theorem for knowledge compilation. In particular, we show that a circuit Z of cliquewidth k can be compiled into a Decomposable Negation Normal Form (dnnf) of size O(918kk2|Z|) and the same runtime. To the best of our knowledge, this is the first result on efficient knowledge compilation parameterized by cliquewidth of a Boolean circuit.