Complementary Knowledge Compilation Using the Hyper Extension Rule

We introduce the concept of Complementary formula (COMF), which is a new and non-equivalent way for Knowledge compilation (KC). Based on the Hyper extension rule (HER) which is an expansion of Extension rule (ER), we design a compilation algorithm which can formula compile each Conjunctive normal form (CNF) formula to complementary Fully complementary connected diagram (c-FCCD), named as C2C (CNF formula to cFCCD). Theoretically, c-FCCD is a kind of complementary formulae of the input formulae and can support all queries and partial transformations in KC map. Experimentally, C2C is competitive with the EPCCL compilers KCER, C2E, UKCHER, DKCHER and IKCHER.