Bounded-Memory Criteria for Streams with Application Time

Bounded-memory computability continues to be in the focus of those areas of AI and databases that deal with feasible computations over streams---be it feasible arithmetical calculations on low-level streams or feasible query answering for declaratively specified queries on relational data streams or even feasible query answering for high-level queries on streams w.r.t. a set of constraints in an ontology such as in the paradigm of Ontology-Based Data Access (OBDA). In classical OBDA, a high-level query is answered by transforming it into a query on data source level. The transformation requires a rewriting step, where knowledge from an ontology is incorporated into the query, followed by an unfolding step with respect to a set of mappings. Given an OBDA setting it is very difficult to decide, whether and how a query can be answered efficiently. In particular it is difficult to decide whether a query can be answered in bounded memory, i.e., in constant space w.r.t. an infinitely growing prefix of a data stream. This work presents criteria for bounded-memory computability of select-project-join (SPJ) queries over streams with application time. Deciding whether an SPJ query can be answered in constant space is easier than for high-level queries, as neither an ontology nor a set of mappings are part of the input. Using the transformation process of classical OBDA, these criteria then can help deciding the efficiency of answering high-level queries on streams.