Recognition of Nested Gates in CNF Formulas

We present a new algorithm to efficiently extract information about nested functional dependencies between variables of a formula in CNF. Our algorithm uses the relation between gate encodings and blocked sets in CNF formulas. Our notion of "gate" emphasizes this relation. The presented algorithm is central to our new tool, cnf2aig, that produces equisatisfiable and-inverter-graphs (AIGs) from CNF formulas. We compare the novel algorithm to earlier approaches and show that the produced AIG are generally more succinct and use less input variables. As the gate-detection is related to the structure of input formulas, we furthermore analyze the gate-detection before and after applying preprocessing techniques.