The finite state machine (FSM) model is commonly used for specifying communication protocols and other types of distributed systems. For an FSM with multiple ports, multiple testers are needed, but the synchronization between inputs from different testers becomes a problem. A synchronizable test sequence of an FSM is a test sequence for which the synchronization problem either does not exist or can be solved by communication between testers. In this paper, we consider two testing strategies for an FSM: port-based testing, which does not allow testers for the FSM to communicate with each other, and group-based testing, which divides ports of the FSM into mutually disjoint groups and allows testers for ports in the same group to communicate with each other. For each type of testing, we define a necessary and sufficient condition under which a test sequence of an FSM is synchronizable and show how to generate a set of testers according to a given test sequence. We also discuss test sequence generation and fault detection, and present the results of empirical studies.