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)


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.


Model Check Tree Language Membership Problem Intermediate Term Tree Transducer 
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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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