The use of blockchain technology has been proposed to provide auditable access control for individual resources. Unlike the case where all resources are owned by a single organization, this work focuses on distributed applications such as business processes and distributed workflows. These applications are often composed of multiple resources/services that are subject to the security and access control policies of different organizational domains. Here, blockchains provide an attractive decentralized solution to provide auditability. However, the underlying access control policies may have event-driven constraints and can be overlapping in terms of the component conditions/rules as well as events. Existing work cannot handle event-driven constraints and also does not sufficiently account for overlaps leading to significant overhead in terms of cost and computation time for evaluating authorizations over the blockchain. In this work, we propose an automata-theoretic approach for generating a cost-efficient composite access control policy. We reduce this composite policy generation problem to the standard weighted set cover problem. We show that the composite policy correctly captures all the local access control policies and reduces the policy evaluation cost over the blockchain. We have implemented the initial prototype of our approach using Ethereum as the underlying blockchain and empirically validated the effectiveness and efficiency of our approach.