It is proved that all Boolean functions can be computed using two memristors. To achieve this, a recursive conjunctive form for Boolean functions is introduced and its universality shown.Introduction: A memristor is a non-volatile two-terminal device, whose resistance can be programmed. It was theoretically described in [1] and recently experimented with by many groups, e.g. [2]. It was shown in [3] that material implication p ! q is the natural logical operation for computing with binary memristors. Thus, if p and q are the states [ B ¼ f0; 1g of two memristors m 1 , m 2 , then storing p ! q as the state of m 2 is regarded as an elementary computational step. Identifying memristors and their states we may thus write

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