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Memristive switches are promising devices for future nonvolatile nanocrossbar memory devices. In particular, complementary resistive switches (CRSs) are the key enabler for passive crossbar array implementation solving the sneak path obstacle. To provide logic along with memory functionality, “material implication” (IMP) was suggested as the basic logic operation for bipolar resistive switches. Here, we show that every bipolar resistive switch as well as CRSs can be considered as an elementary IMP logic unit and can systematically be understood in terms of finite-state machines, i.e., either a Moore or a Mealy machine. We prove our assumptions by measurements, which make the IMP capability evident. Local fusion of logic and memory functions in crossbar arrays becomes feasible for CRS arrays, particularly for the suggested stacked topology, which offers even more common Boolean logic operations such as and and nor .