A machine model for data stream computation

We consider online and space-bounded computations in the data stream processing model where a stream is a sequence of records of the form (i, 1) signifying insertion of item i, or, (i,−1), signifying deletion of item i, where, i ∈ {1, 2, . . . , n}. This model finds applications in network monitoring, approximate query answering in databases, computational geometry, where, items signify points in d-dimensional space, graph streams, where, items signify edges of a streaming graph and compressed sensing. We abstract computations over data streams using the stream automata model of computation. Our main result is that a certain natural generalization of the transition function of any stream automaton is essentially a linear mapping. This is used to derive space lower bounds for deterministic data stream computations.