TY - GEN
T1 - Cliquewidth and knowledge compilation
AU - Razgon, Igor
AU - Petke, Justyna
PY - 2013/7/15
Y1 - 2013/7/15
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84879985029
U2 - 10.1007/978-3-642-39071-5_25
DO - 10.1007/978-3-642-39071-5_25
M3 - Conference contribution
AN - SCOPUS:84879985029
SN - 9783642390708
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 335
EP - 350
BT - Theory and Applications of Satisfiability Testing, SAT 2013 - 16th International Conference, Proceedings
T2 - 16th International Conference on Theory and Applications of Satisfiability Testing, SAT 2013
Y2 - 8 July 2013 through 12 July 2013
ER -