Lexicalized Non-Local MCTAG with Dominance Links is NP-Complete

Lucas Champollion

    Research output: Contribution to journalArticle

    Abstract

    An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456-472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate.

    Original languageEnglish (US)
    Pages (from-to)343-359
    Number of pages17
    JournalJournal of Logic, Language and Information
    Volume20
    Issue number3
    DOIs
    StatePublished - Jul 2011

    Fingerprint

    Computational linguistics
    grammar
    Hardness
    computational linguistics
    candidacy
    Tree Adjoining Grammar

    Keywords

    • Dominance links
    • Lexicalization
    • MCTAG
    • Mildly context-sensitive
    • NP-complete
    • Scrambling
    • Tree Adjoining Grammar

    ASJC Scopus subject areas

    • Linguistics and Language
    • Philosophy
    • Computer Science (miscellaneous)

    Cite this

    Lexicalized Non-Local MCTAG with Dominance Links is NP-Complete. / Champollion, Lucas.

    In: Journal of Logic, Language and Information, Vol. 20, No. 3, 07.2011, p. 343-359.

    Research output: Contribution to journalArticle

    @article{10c549ddcb7e4abfad2ff4eae8aa8fa3,
    title = "Lexicalized Non-Local MCTAG with Dominance Links is NP-Complete",
    abstract = "An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456-472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate.",
    keywords = "Dominance links, Lexicalization, MCTAG, Mildly context-sensitive, NP-complete, Scrambling, Tree Adjoining Grammar",
    author = "Lucas Champollion",
    year = "2011",
    month = "7",
    doi = "10.1007/s10849-011-9133-1",
    language = "English (US)",
    volume = "20",
    pages = "343--359",
    journal = "Journal of Logic, Language and Information",
    issn = "0925-8531",
    publisher = "Springer Netherlands",
    number = "3",

    }

    TY - JOUR

    T1 - Lexicalized Non-Local MCTAG with Dominance Links is NP-Complete

    AU - Champollion, Lucas

    PY - 2011/7

    Y1 - 2011/7

    N2 - An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456-472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate.

    AB - An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456-472, 1986), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate.

    KW - Dominance links

    KW - Lexicalization

    KW - MCTAG

    KW - Mildly context-sensitive

    KW - NP-complete

    KW - Scrambling

    KW - Tree Adjoining Grammar

    UR - http://www.scopus.com/inward/record.url?scp=80051920500&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=80051920500&partnerID=8YFLogxK

    U2 - 10.1007/s10849-011-9133-1

    DO - 10.1007/s10849-011-9133-1

    M3 - Article

    AN - SCOPUS:80051920500

    VL - 20

    SP - 343

    EP - 359

    JO - Journal of Logic, Language and Information

    JF - Journal of Logic, Language and Information

    SN - 0925-8531

    IS - 3

    ER -