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This paper gives a brief overview of computation models for data stream processing, and it introduces a new model for multi-pass processing of multiple streams, the so-called mp2s-automata. Two algorithms for solving the set disjointness problem with these automata are presented. The main technical contribution of this paper is the proof of a lower bound on the size of memory and the number of heads that are required for solving the set disjointness problem with mp2s-automata.