Reconfigurable manufacturing systems (RMS) support flexibility in the product variety and the configuration of the manufacturing system itself in order to enable quick adjustments to new products and production requirements. As a consequence, an essential feature of RMS is their ability to rapidly modify the control strategy during run-time. In this paper, the particular problem of changing the specified operation of a RMS, whose logical behaviour is modelled as a finite state automaton, is addressed. The notion of reconfigurability of specifications (RoS) is introduced and it is shown that the stated reconfiguration problem can be formulated as a controlled language convergence problem. In addition, algorithms for the verification of RoS and the construction of a reconfiguration supervisor are proposed. The supervisor is realised in a modular way which facilitates the extension by new configurations. Finally, it is shown that a supremal nonblocking and controllable strict subautomaton of the plant automaton that fulfils RoS exists in case RoS is violated for the plant automaton itself and an algorithm for the computation of this strict subautomaton is presented. The developed concepts and results are illustrated by a manufacturing cell example.