2018/07/11 by Florent Capelli, Stefan Mengel, Capelli, Florent +1
Computer Science · #Advanced Graph Theory Research #Computational Complexity (cs.CC) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Formal Methods in Verification
paper · pdf · doi:10.48550/arxiv.1807.04263
openalex publication_date 2018/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize many results concerning the tractability of SAT and #SAT on bounded treewidth CNF-formula in the context of Quantified Boolean Formulas (QBF). To this end, we start by studying the notion of width for OBDD and observe that the blow up in size while existentially or universally projecting a block of variables in an OBDD only affects its width. We then generalize this notion of width to the more general representation of structured (deterministic) DNNF and give a similar algorithm to existentially or universally project a block of variables. Using a well-known algorithm transforming bounded treewidth CNF formula into deterministic DNNF, we are able to generalize this connection to quantified CNF which gives us as a byproduct that one can count the number of models of a bounded treewidth and bounded quantifier alternation quantified CNF in FPT time. We also give an extensive study of bounded width d-DNNF and proves the optimality of several of our results.