Reconfigurable logic devices and methods of programming the devices are disclosed. The logic device includes a look-up table (LUT) and at least one storage element configured for sampling LUT output signals. The LUT comprises a plurality of input signals, an array of programmable impedance devices operably coupled to the input signals, and the LUT output signals. Each programmable impedance device in the array includes a first electrode operably coupled to one of the input signal, a second electrode disposed to form a junction wherein the second electrode at least partially overlaps the first electrode, and a programmable material disposed between the first electrode and the second electrode. The programmable material operably couples the first electrode and the second electrode such that each programmable impedance device exhibits a non-volatile programmable impedance. The array may be configured as a one-dimensional or two-dimensional array.