A distributed system includes full and partial replicas of a set of data items that may be inserted, modified, or deleted by any replica. Replicas may occasionally synchronize with other arbitrarily chosen replicas to learn about updates. A replica's knowledge includes one or more knowledge fragments, where each fragment indicates a set of items. A type of knowledge fragment, called a star knowledge fragment, contains versions associated with all items in the system. Star knowledge fragments are compact because the set of items stored at a replica need not be explicitly listed. Once all replicas know of all updates in the system, partial and full replicas will have the same compact star knowledge fragment.