State machines using resistivity-sensitive memory elements are disclosed. The state machine includes a next state logic comprising a non-volatile memory including a resistivity-sensitive memory element and receiving an input, a state storage device connected to the next state logic including a connection to provide a state of the state machine to the next state logic, and an output connect to the state register to output the state of the state machine. The resistivity-sensitive memory elements may be two-terminal resistivity-sensitive memory elements. The two-terminal resistivity-sensitive memory elements may store data as a plurality of conductivity profiles that can be non-destructively read by applying a read voltage across the terminals of the memory elements, and new data can be written by applying a write voltage across the terminals. The two-terminal resistivity-sensitive memory elements retain stored data in the absence of power and may be configured into a two-terminal cross-point memory array.