Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2010-04

AUTHORS

Makoto Kanazawa

ABSTRACT

Second-order abstract categorial grammars (de Groote in Association for computational linguistics, 39th annual meeting and 10th conference of the European chapter, proceedings of the conference, pp. 148–155, 2001) and hyperedge replacement grammars (Bauderon and Courcelle in Math Syst Theory 20:83–127, 1987; Habel and Kreowski in STACS 87: 4th Annual symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 247, Springer, Berlin, pp 207–219, 1987) are two natural ways of generalizing “context-free” grammar formalisms for string and tree languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. in Theor Comput Sci 88:191–229, 1991) or linear context-free rewriting systems (Weir in Characterizing mildly context-sensitive grammar formalisms, University of Pennsylvania, 1988). In this paper, we give a simple, direct proof of the fact that second-order ACGs are simulated by hyperedge replacement grammars, which implies that the string and tree generating power of the former is included in that of the latter. The normal form for tree-generating hyperedge replacement grammars given by Engelfriet and Maneth (Graph transformation. Lecture notes in computer science, vol 1764. Springer, Berlin, pp 15–29, 2000) can then be used to show that the tree generating power of second-order ACGs is exactly the same as that of hyperedge replacement grammars. More... »

PAGES

137-161

References to SciGraph publications

  • 1987-12. Graph expressions and graph rewritings in MATHEMATICAL SYSTEMS THEORY
  • 1987. Some structural aspects of hypergraph languages generated by hyperedge replacement in STACS 87
  • 1970-09. Mappings and grammars on trees in MATHEMATICAL SYSTEMS THEORY
  • 2000. Tree Languages Generated by Context-Free Graph Grammars in THEORY AND APPLICATION OF GRAPH TRANSFORMATIONS
  • 1997. Context-Free Graph Grammars in HANDBOOK OF FORMAL LANGUAGES
  • 1997. Tree Languages in HANDBOOK OF FORMAL LANGUAGES
  • 2004-03. On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms in JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
  • 1990-04. The complexity of graph languages generated by hyperedge replacement in ACTA INFORMATICA
  • 2005. The Complexity and Generative Capacity of Lexicalized Abstract Categorial Grammars in LOGICAL ASPECTS OF COMPUTATIONAL LINGUISTICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10849-009-9109-6

    DOI

    http://dx.doi.org/10.1007/s10849-009-9109-6

    DIMENSIONS

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