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Querying streams using regular expressions: some semantics, decidability, and efficiency issues

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Abstract

This paper analyzes the decidability and complexity problems that arise when matching regular expressions on infinite streams of sets of symbols. We show that in important application domains, several apparently obvious semantics lead to detecting spurious events (events that are mere artifacts of the semantics) or to missing events of potential interest. We single out a class of semantics, of interest in many applications, which we dub use-and-throw: In a use-and-throw semantics, an elementary event can participate in the creation of at most one detected complex event. Many areas of research have identified this as a desirable requirement (we give the examples of databases and video surveillance), but hitherto there has been no systematic study of the characteristics of these semantics, in particular their decidability and algorithmic complexity. This paper is meant to provide at least some initial answers on this subject. We analyze several semantics, provide polynomial algorithms for them, and prove their correctness and their properties.

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Notes

  1. A definition of the signature of an event will be given shortly; for the sake of this example, the intuitive notion of signature as the marker of an event “type” will suffice.

  2. The intersection is defined stream- and expression-wise in the obvious way.

  3. In this section, “semantics” will always signify “use-and-throw semantics”.

  4. We shall use syntactic sugar as necessary. So, we define \(a\ge {b}\) as \((a>b\vee {a}=b)\), \(\forall x.\psi \) as \(\lnot \exists {x}.\lnot \psi \), etc.

  5. We shall see in the next section examples in which the predicate P contains a term of the form \(\pi \diamond \pi '\ne \emptyset \). In this case, we are not interested in checking paths such that \({\mathtt{str}}({\pi '})>{\mathtt{end}}({\pi })\).

  6. The expression has been slightly modified with respect to the original in order to simplify the presentation without cluttering it with superfluous details, cf. [53].

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  1. Escuela Politécnica Superior, Universidad Autónoma de Madrid, Madrid, Spain

    Simone Santini

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Correspondence to Simone Santini.

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This work was supported in part by the Ministerio de Educación y Ciencia under the Grant No. TIN2013-47090-C3-2, VoxPopuli, Efficient reputation analysis, propagation and recommendation in social network environments.

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Santini, S. Querying streams using regular expressions: some semantics, decidability, and efficiency issues. The VLDB Journal 24, 801–821 (2015). https://doi.org/10.1007/s00778-015-0402-5

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