Model Counting for 2SAT Based on Graphs by Matrix Operators

Counting the models of Boolean formulae is known to be intractable but pops up often in diverse areas. We focus in a restricted version of the problem. In particular, our results are based on matrix operators and Hadamard product for counting models of Boolean formulae consisting of chains and embedded cycles. We obtain an efficient algorithm such that the input is a Boolean formula Σ in 2-CNF and the output can be either a charged Boolean formula Σ′ simpler than Σ or the number of models of Σ (the charge of a Boolean formula Σ is introduced as a vector in N, which contains information about the number of models of Σ). In the latter case, Σ belongs to a tractable class of Boolean formulae in 2CNF for #SAT that contains the classes 2μ-2SAT and Acyclic-2HORN.