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Colored Nested Words

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

Nested words allow modeling of linear and hierarchical structure in data, and nested word automata are special kinds of pushdown automata whose push/pop actions are directed by the hierarchical structure in the input nested word. The resulting class of regular languages of nested words has many appealing theoretical properties, and has found many applications, including model checking of procedural programs. In the nested word model, the hierarchical matching of open- and close- tags must be properly nested, and this is not the case, for instance, in program executions in presence of exceptions. This limitation of nested words narrows its model checking applications to programs with no exceptions.

We introduce the model of colored nested words which allows such hierarchical structures with mismatches. We say that a language of colored nested words is regular if the language obtained by inserting the missing closing tags is a well-colored regular language of nested words. We define an automata model that accepts regular languages of colored nested words. These automata can execute restricted forms of \(\varepsilon \)-pop transitions. We provide an equivalent grammar characterization and show that the class of regular languages of colored nested words has the same appealing closure and decidability properties as nested words, thus removing the restriction of programs to be exception-free in order to be amenable for model checking, via the nested words paradigm.

This research was supported by US NSF grant CCF-1138996.

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Notes

  1. 1.

    Our notation for internal letters, marking a letter with a dot as in \(\dot{a}\), differs slightly from nested words literature which uses simply a. When there is no risk of confusion we may use un-dotted versions too.

  2. 2.

    Pending returns (\({\,\rightharpoondown \,}\)) by definition share a source.

  3. 3.

    Note that a blind cna is still different than a traditional nested word automaton, as it has the means to skip all the unmatched calls and arrive to the matching call.

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Authors and Affiliations

  1. Department of Computer and Information Sciences, University of Pennsylvania, Philadelphia, PA, USA

    Rajeev Alur & Dana Fisman

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  1. Rajeev Alur
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  2. Dana Fisman
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Correspondence to Dana Fisman .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Alur, R., Fisman, D. (2016). Colored Nested Words. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_11

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  • Print ISBN: 978-3-319-29999-0

  • Online ISBN: 978-3-319-30000-9

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