While reading up on memristors and their applications, I realized memristors and diodes have a lot in common. Putting current through in one direction will have a very low resistance (eventually). Putting current through the opposite way will have a very high resistance (eventually).

So a memristor will have a slow response to a forward current until it reaches a low resistance - it may start off high, but after a while it will decrease to it's minimum. Similiar with reverse current - it may start off low resistance, but will eventually end up high resistance.

Diodes will react much faster. However, diodes also require a minimum forward voltage before they start conducting. They are also highly non-linear near their forward voltage point.

But these two devices are close enough to build similar logic gates. Specifically, a Wired-OR and Wired-AND that is constructed with diodes can also be constructed with memreistors. However, in this type of arrangement, you can't make a NOT gate. I'm still looking into other ways of using memristors in logic gates which do include the NOT function, but they are more complicated.

I should really get a good SPICE model of a memristor built so I can prove these ideas out.