A non-volatile programmable circuit configurable to perform logic functions, is provided. The programmable circuit can employ two-terminal non-volatile memory devices to store information, thereby mitigating or avoiding disturbance of programmed data in the absence of external power. Two-terminal resistive switching memory devices having high current on/off ratios and fast switching times can also be employed for high performance, and facilitating a high density array. For look-up table applications, input/output response times can be several nanoseconds or less, facilitating much faster response times than a memory array access for retrieving stored data.