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In this paper we study automatic composition synthesis of e-Services, based on automated reasoning. We represent the behavior of an e-Service in terms of a deterministic transition syst (or a finite state machine), in which for each action the role of the e-Service, either as initiator or as servant, is highlighted. In this setting we present an algorithm based on satisfiability in a variant of Propositional Dynamic Logic that solves the automatic composition probl. Specifically, given (i) a possibly incomplete specification of the sequences of actions that a client would like to realize, and (ii) a set of available e-Services, our technique synthesizes a composite e-Service that (i) uses only the available e-Services and (ii) interacts with the client "in accordance" to the given specification. We also study the computational complexity of the proposed algorithm.