The Tree-Generative Capacity of Combinatory Categorial Grammars

Authors Marco Kuhlmann , Andreas Maletti , Lena Katharina Schiffer

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Marco Kuhlmann
  • Dept. of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden
Andreas Maletti
  • Institute for Computer Science, Universität Leipzig, P.O. box 100 920, D-04009 Leipzig, Germany
Lena Katharina Schiffer
  • Institute for Computer Science, Universität Leipzig, P.O. box 100 920, D-04009 Leipzig, Germany

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Marco Kuhlmann, Andreas Maletti, and Lena Katharina Schiffer. The Tree-Generative Capacity of Combinatory Categorial Grammars. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The generative capacity of combinatory categorial grammars as acceptors of tree languages is investigated. It is demonstrated that the such obtained tree languages can also be generated by simple monadic context-free tree grammars. However, the subclass of pure combinatory categorial grammars cannot even accept all regular tree languages. Additionally, the tree languages accepted by combinatory categorial grammars with limited rule degrees are characterized: If only application rules are allowed, then they can accept only a proper subset of the regular tree languages, whereas they can accept exactly the regular tree languages once first degree composition rules are permitted.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Tree languages
  • Theory of computation → Grammars and context-free languages
  • Computing methodologies
  • Computing methodologies → Artificial intelligence
  • Computing methodologies → Natural language processing
  • Combinatory Categorial Grammar
  • Regular Tree Language
  • Linear Context-free Tree Language


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