Finite state logic machines can be realized by pump-probe spectroscopic experiments on an isolated molecule. The most elaborate setup, a Turing machine, can be programmed to carry out a specific computation. We argue that a molecule can be similarly programmed, and provide examples using two photon spectroscopies. The states of the molecule serve as the possible states of the head of the Turing machine and the physics of the problem determines the possible instructions of the program. The tape is written in an alphabet that allows the listing of the different pump and probe signals that are applied in a given experiment. Different experiments using the same set of molecular levels correspond to different tapes that can be read and processed by the same head and program. The analogy to a Turing machine is not a mechanical one and is not completely molecular because the tape is not part of the molecular,machine. We therefore also discuss molecular finite state machines, such as sequential devices, for which the tape is not part of the machine. Nonmolecular tapes allow for quite long input sequences with a rich alphabet (at the level of 7 bits) and laser pulse:shaping experiments provide concrete examples. Single molecule spectroscopies show that a single molecule can be repeatedly cycled through a logical operation.