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We consider a compositional method for the verification of component-based systems described in a subset of the BIP language encompassing multi-party interactions. The method is based on the use of two kinds of invariants. Component invariants are over-approximations of components' reach ability sets. Interaction invariants are constraints on the states of components involved in interactions. In this paper we propose fixed point characterization for computing interaction invariants. We also propose a new technique that takes the incremental design of the system into account. In many situations, the technique will help to avoid redoing all the verification process each time an interaction is added in the design. Our two techniques have been implemented as extension of the D-Finder toolset. The result has been applied to check deadlock-freedom on several case studies. Our experiments show that our new methodology is generally much faster than existing ones.