Probabilistic data structures are used in applications that manage large datasets due to their time and space efficiency. These applications can accommodate approximate results from probabilistic data structures and replicated systems that use them can take advantage of the efficiency gained from weaker synchronization and consistency among replicas.

In this paper, we propose conflict-free replicated data types (CRDTs) for probabilistic data structures with approximate membership queries. Specifically, we introduce Conflict-Free Replicated Bloom Filters and Conflict-Free Replicated Cuckoo Filters, which are the conflict-free versions of traditional Bloom and Cuckoo filters. We provide implementations of these data structures in an open-source repository and present an evaluation of the approximate query results across various workload and replica synchronization configurations.