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    Decomposing quantified conjunctive (or disjunctive) formulas

    Chen, Hubie and Dalmau, V. (2016) Decomposing quantified conjunctive (or disjunctive) formulas. SIAM Journal on Computing 45 (6), pp. 2066-2086. ISSN 0097-5397.

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    Abstract

    Model checking---deciding if a logical sentence holds on a structure---is a basic computational task that is well known to be intractable in general. For first-order logic on finite structures, it is PSPACE-complete, and the natural evaluation algorithm exhibits exponential dependence on the formula. We study model checking on the quantified conjunctive fragment of first-order logic, namely, prenex sentences having a purely conjunctive quantifier-free part. Following a number of works, we associate a graph to the quantifier-free part; each sentence then induces a prefixed graph, a quantifier prefix paired with a graph on its variables. We give a comprehensive classification of the sets of prefixed graphs on which model checking is tractable based on a novel generalization of treewidth that generalizes and places into a unified framework a number of existing results.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Hubert Chen
    Date Deposited: 20 Apr 2018 13:16
    Last Modified: 04 Feb 2020 15:02
    URI: http://eprints.bbk.ac.uk/id/eprint/22144

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