Backdoor Sets of Quantified Boolean Formulas
Journal of Automated Reasoning
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Algorithms for propositional model counting
Journal of Discrete Algorithms
Exploiting problem structure for solution counting
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Computation of renameable Horn backdoors
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Backdoors to tractable answer-set programming
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The Multivariate Algorithmic Revolution and Beyond
Strong backdoors to nested satisfiability
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Homomorphic hashing for sparse coefficient extraction
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Satisfiability of acyclic and almost acyclic CNF formulas
Theoretical Computer Science
Hi-index | 0.01 |
We propose an exact algorithm for counting the models of propositional formulas in conjunctive normal form. Our algorithm is based on the detection of strong backdoor sets of bounded size; each instantiation of the variables of a strong backdoor set puts the given formula into a class of formulas for which models can be counted in polynomial time. For the backdoor set detection we utilize an efficient vertex cover algorithm applied to a certain “obstruction graph” that we associate with the given formula. This approach gives rise to a new hardness index for formulas, the clustering-width. Our algorithm runs in uniform polynomial time on formulas with bounded clustering-width. It is known that the number of models of formulas with bounded clique-width, bounded treewidth, or bounded branchwidth can be computed in polynomial time; these graph parameters are applied to formulas via certain (hyper)graphs associated with formulas. We show that clustering-width and the other parameters mentioned are incomparable: there are formulas with bounded clustering-width and arbitrarily large clique-width, treewidth, and branchwidth. Conversely, there are formulas with arbitrarily large clustering-width and bounded clique-width, treewidth, and branchwidth.