Abstract Interpretation of Indexed Grammars

  • Marco CampionEmail author
  • Mila Dalla Preda
  • Roberto Giacobazzi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11822)


Indexed grammars are a generalization of context-free grammars and recognize a proper subset of context-sensitive languages. The class of languages recognized by indexed grammars are called indexed languages and they correspond to the languages recognized by nested stack automata. For example indexed grammars can recognize the language Open image in new window which is not context-free, but they cannot recognize Open image in new window which is context-sensitive. Indexed grammars identify a set of languages that are more expressive than context-free languages, while having decidability results that lie in between the ones of context-free and context-sensitive languages. In this work we study indexed grammars in order to formalize the relation between indexed languages and the other classes of languages in the Chomsky hierarchy. To this end, we provide a fixpoint characterization of the languages recognized by an indexed grammar and we study possible ways to abstract, in the abstract interpretation sense, these languages and their grammars into context-free and regular languages.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Marco Campion
    • 1
    Email author
  • Mila Dalla Preda
    • 1
  • Roberto Giacobazzi
    • 1
  1. 1.Dipartimento di InformaticaUniversity of VeronaVeronaItaly

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