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The global interaction behavior in message-based systems can be specified as a finite-state machine defining acceptable sequences of messages exchanged by a group of peers. Realizability analysis determines if there exist local implementations for each peer, such that their composition produces exactly the intended global behavior. Although there are existing sufficient conditions for realizability, we show that these earlier results all fail for a particular class of specifications called arbitrary-initiator protocols. We present a novel algorithm for deciding realizability by computing a finite-state model that keeps track of the information about the global state of a conversation protocol that each peer can deduce from the messages it sends and receives. By searching for disagreements between each peer's deduced states, we provide a sound analysis for realizability that correctly classifies realizability of arbitrary-initiator protocols.