Satisfiability and relevance for queries over active documents

ManyWeb applications are based on dynamic interactions between Web components exchanging flows of information. Such a situation arises for instance in mashup systems [22] or when monitoring distributed autonomous systems [6]. This is a challenging problem that has generated recently a lot of attention; see Web 2.0 [38]. For capturing interactions between Web components, we use active documents interacting with the rest of the world via streams of updates. Their input streams specify updates to the document (in the spirit of RSS feeds), whereas their output streams are defined by queries on the document. In most of the paper, the focus is on input streams where the updates are only insertions, although we do consider also deletions. We introduce and study two fundamental concepts in this setting, namely, satisfiability and relevance. Some fact is satisfiable for an active document and a query if it has a chance to be in the result of the query in some future state. Given an active document and a query, a call in the document is relevant if the data brought by this call has a chance to impact the answer to the query. We analyze the complexity of computing satisfiability in our core model (insertions only) and for extensions (e.g., with deletions). We also analyze the complexity of computing relevance in the core model.