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    Relational expressive power of constraint query languages

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    The expressive power of first-order query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals. Furthermore, noting that relational queries exhibit several forms of genericity, we establish a number of collapse results of the following form: The class of generic Boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus (with or without an order relation). We prove such results for both the natural and active-domain semantics. As a consequence, the relational calculus augmented with polynomial inequalities expresses the same classes of generic Boolean queries under both the natural and active-domain semantics.In the course of proving these results for the active-domin semantics, we establish Ramsey-type theorems saying that any query involving certain kinds of constraints coincides with a constraint-free query on databases whose elements come from a certain infinite subset of the domain. To prove the collapse results for the natural semantics, we make use of techniques from nonstandard analysis and from the model theory of ordered structures.

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    Description

    Title : Relational expressive power of constraint query languages
    Author(s) : Michael Benedikt, Guozhu Dong, Leonid Libkin, Limsoon Wong
    Abstract : The expressive power of first-order query languages with several classes of equality and inequality constraints is studied in this paper. We settle the conjecture that recursive queries such as parity test and transitive closure cannot be expressed in the relational calculus augmented with polynomial inequality constraints over the reals. Furthermore, noting that relational queries exhibit several forms of genericity, we establish a number of collapse results of the following form: The class of generic Boolean queries expressible in the relational calculus augmented with a given class of constraints coincides with the class of queries expressible in the relational calculus (with or without an order relation). We prove such results for both the natural and active-domain semantics. As a consequence, the relational calculus augmented with polynomial inequalities expresses the same classes of generic Boolean queries under both the natural and active-domain semantics.In the course of proving these results for the active-domin semantics, we establish Ramsey-type theorems saying that any query involving certain kinds of constraints coincides with a constraint-free query on databases whose elements come from a certain infinite subset of the domain. To prove the collapse results for the natural semantics, we make use of techniques from nonstandard analysis and from the model theory of ordered structures.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 1998

    Affiliations Dept of Computer Science, National University of Singapore
    Journal : Journal of the ACM
    Volume : 45
    Issue : 1
    Publisher : ACM
    Pages : 1 - 34
    Url : http://portal.acm.org/citation.cfm?doid=273865.273870
    Doi : 10.1145/273865.273870

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    Limsoon's Peer Evaluation activity

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