Stateful implication logic with memristors

In this paper computation with memristors is studied in terms of how many memristors are needed to perform a given logic operation. It has been shown that memristors are naturally suited for performing implication logic (combination of implication and false operation) instead of Boolean logic. Also, it should be noted that a memristor can be used as both a logic gate and a latch (stateful logic). Being functionally complete, implication logic can be used to compute any Boolean function. However, by performing implication logic with stateful devices, storage of intermediate results requires additional memristors to keep data yet to be used from being written over. This paper describes an effective way to compute any Boolean function with a small number of memristors. Also, the length of the corresponding computing sequence is considered.