Alternative computing approaches that interface readily with physical systems are well suited for embedded control of those systems. We demonstrate finite state machines implemented as pneumatic circuits of microfluidic valves and use these controllers to direct microfluidic liquid handling procedures on the same chip. These monolithic integrated systems require only power to be supplied externally, in the form of a vacuum source. User input can be provided directly to the chip by covering pneumatic ports with a finger. State machines with up to four bits of state memory are demonstrated, and next-state combinational logic can be fully reprogrammed by changing the hole-punch pattern on a membrane in the chip. These pneumatic computers demonstrate a framework for the embedded control of physical systems and open a path to stand-alone lab-on-a-chip devices capable of highly complex functionality.