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Unsafe Order-2 Tree Languages Are Context-Sensitive

  • Naoki Kobayashi
  • Kazuhiro Inaba
  • Takeshi Tsukada
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)

Abstract

Higher-order grammars have been extensively studied in 1980’s and interests in them have revived recently in the context of higher-order model checking and program verification, where higherorder grammars are used as models of higher-order functional programs. A lot of theoretical questions remain open, however, for unsafe higherorder grammars (grammars without the so-called safety condition). In this paper, we show that any tree languages generated by order-2 unsafe grammars are context-sensitive. This also implies that any unsafe order-3 word languages are context-sensitive. The proof involves novel technique based on typed lambda-calculus, such as type-based grammar transformation.

Keywords

Model Check Tree Language Membership Problem Intermediate Term Tree Transducer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Naoki Kobayashi
    • 1
  • Kazuhiro Inaba
    • 2
  • Takeshi Tsukada
    • 3
    • 4
  1. 1.The University of TokyoJapan
  2. 2.Google Inc.USA
  3. 3.University of OxfordUK
  4. 4.JSPS Postdoctoral Fellow for Research AbroadJapan

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