Transformations into Normal Forms for Quantified Circuits

Encoding Nested Boolean Functions as Quantified Boolean Formulas

“…As suggested informally in [8] and explained in Section 6 in more detail, it is easy to transform quantified Boolean formulas into equivalent nested Boolean functions with a linear number of function definitions by simulating quantifiers. With the QBF encoding pattern for nested formula instantiations that we develop in this paper, we obtain an equivalencepreserving transformation also in the other direction from NBF to QBF in linear time, which can be a valuable tool for proving expressiveness results.…”

“…With the QBF encoding pattern for nested formula instantiations that we develop in this paper, we obtain an equivalencepreserving transformation also in the other direction from NBF to QBF in linear time, which can be a valuable tool for proving expressiveness results. For example, we have been able to show in [8] close relationships between QBF and classes of quantified circuits (Boolean circuits with additional quantifier nodes not necessarily in prenex form), and the proofs of these results rely heavily on the NBF to QBF transformation that we are now going to establish ( [8] anticipates that transformation without further details and references a preliminary workshop version of the paper at hand).…”