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Abstract Interpretation of Indexed Grammars

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Static Analysis (SAS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11822))

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Abstract

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 which is not context-free, but they cannot recognize 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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Authors and Affiliations

  1. Dipartimento di Informatica, University of Verona, Verona, Italy

    Marco Campion, Mila Dalla Preda & Roberto Giacobazzi

Authors
  1. Marco Campion
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  2. Mila Dalla Preda
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  3. Roberto Giacobazzi
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Correspondence to Marco Campion .

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Editors and Affiliations

  1. University of Colorado, Boulder, CO, USA

    Bor-Yuh Evan Chang

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Campion, M., Dalla Preda, M., Giacobazzi, R. (2019). Abstract Interpretation of Indexed Grammars. In: Chang, BY. (eds) Static Analysis. SAS 2019. Lecture Notes in Computer Science(), vol 11822. Springer, Cham. https://doi.org/10.1007/978-3-030-32304-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-32304-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32303-5

  • Online ISBN: 978-3-030-32304-2

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