  The requirement of a language to be conditionally decomposable is imposed on
a specification language in the coordination supervisory control framework of
discrete-event systems. In this paper, we present a polynomial-time algorithm
for the verification whether a language is conditionally decomposable with
respect to given alphabets. Moreover, we also present a polynomial-time
algorithm to extend the common alphabet so that the language becomes
conditionally decomposable. A relationship of conditional decomposability to
nonblockingness of modular discrete-event systems is also discussed in this
paper in the general settings. It is shown that conditional decomposability is
a weaker condition than nonblockingness.
