Context-Free Categorical Grammars

  • Authors:

  • Michel Bauderon;Rui Chen;Olivier Ly

  • Affiliations:

  • Université de Bordeaux - LaBRI CNRS, Talence, France 33405 and Zhongnan University of Economics and Law, Hongshan Wuhan, China 430073;Université de Bordeaux - LaBRI CNRS, Talence, France 33405 and Zhongnan University of Economics and Law, Hongshan Wuhan, China 430073;Université de Bordeaux - LaBRI CNRS, Talence, France 33405 and Zhongnan University of Economics and Law, Hongshan Wuhan, China 430073

  • Venue:
  • CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
  • Year:
  • 2009

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Abstract

We define generic categorical notions of rewriting and grammar, using two basic operations, pullback and pushout, and show that these categorical grammars are intrinsically context-free in the sense of Courcelle. We then specialise to various settings, including classical word grammars, hyperedge replacement grammars or node-replacement grammars. We show that some languages which are classical counter-example to context-freeness become context-free within this new framework.