Partial states are states in which the truth value of one or more propositions is unknown. Such states are usually generated in regression and represent not a single state but rather a set of states. Because of this, a new partial state can be a subset of another existent partial state, phenomenon known as subsumption of states. Subsumed states can be pruned as if they were a duplicate. However, regular duplicate detection methods cannot detect such cases. Furthermore, subsumption of states also occurs when forward and backward search algorithms are integrated into a bidirectional planner. In these cases, the forward frontier contains only complete states and the backward frontier will often contain partial states. In this work, we analyze the impact that subsumption of states has on search and propose methods for duplicate detection and detection of collision of frontiers.