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As a structural object of Petri nets, siphons play a significant role in the development of deadlock prevention policies for resource allocation systems. Elementary siphons are a novel methodology in Petri nets, which have been extensively studied in siphon-based liveness-enforcing supervisor designs. This paper aims to extend elementary siphons to generalized Petri nets. It can find a set of reasonable and compact elementary siphons. For a class of generalized Petri nets, the concept of augmented siphons is proposed to obtain a set of augmented elementary siphons by thoroughly investigating the structure information. The controllability of augmented dependent siphons is proposed on condition that their augmented elementary siphons are properly supervised. Finally, an example is used to illustrate the proposed method and indicate its advantages.