Cliquewidth and Knowledge Compilation
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(918k k 2|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.
KeywordsBoolean Function Tree Decomposition Primal Graph Argumentation Framework Binary Decision Diagram
Unable to display preview. Download preview PDF.
- 5.Darwiche, A.: Sdd: A new canonical representation of propositional knowledge bases. In: IJCAI, pp. 819–826 (2011)Google Scholar
- 7.Dvorák, W., Szeider, S., Woltran, S.: Reasoning in argumentation frameworks of bounded clique-width. In: COMMA, pp. 219–230 (2010)Google Scholar
- 14.Jha, A.K., Suciu, D.: On the tractability of query compilation and bounded treewidth. In: ICDT, pp. 249–261 (2012)Google Scholar