Abstract In the Supervisory Control Theory, originally presented by Ramadge and Wonham, Ramadge and Wonham (1989), an important property is controllability. The definition of controllability as originally presented assumed equal event sets, alphabets, in the specification and the plant. When this assumption does not hold, it has been argued that the differences in the alphabets can easily be removed. However, no matter how we choose to handle the differences, pursuing verification with the original definition will lead to false conjectures in some cases. A few examples on this is presented in this paper. In order to overcome the problem, a generalized controllability definition, allowing non-equal alphabets, is presented. It is of great importance to be able to verify controllability of subsystems with different alphabets when exploiting the modularity of discrete event systems for computationally efficient verification and synthesis.
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