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For deadlock avoidance in automated manufacturing systems (AMSs), it is desired that a deadlock control policy is maximally permissive. However, up to now, the tractability problem of deadlock avoidance in AMSs is still open. This paper conducts study on the tractability problem of deadlock avoidance for the general sequential resource allocation problem with each step requiring a single resource. An AMS is modeled by colored resource-oriented Petri net (CROPN). Based on the model, necessary and sufficient condition, under which the deadlock avoidance problem is tractable, is presented. At the same time, a one step look-ahead control policy is presented.