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Language and Automata Theory and Applications

LATA 2016: Language and Automata Theory and Applications pp 579–591Cite as

Reversible Shrinking Two-Pushdown Automata

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

Abstract

The deterministic shrinking two-pushdown automata characterize the deterministic growing context-sensitive languages, known to be the Church-Rosser languages. Here, we initiate the investigation of reversible two-pushdown automata, RTPDAs, in particular the shrinking variant. We show that as with the deterministic version, shrinking and length-reducing RTPDAs are equivalent. We then give a separation of the deterministic and reversible shrinking two-pushdown automata, and prove that these are incomparable with the (deterministic) context-free languages. We further show that the properties of emptiness, (in)finiteness, universality, inclusion, equivalence, regularity, and context-freeness are not even semi-decidable for shrinking RTPDAs.

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Notes

  1. 1.

    At least when considered as language acceptors—for functions the picture is somewhat more complex [1].

  2. 2.

    The extension to \((Q\cup \varGamma \cup \{\bot \})^*\) is defined by \(\varphi (xy)=\varphi (x)+\varphi (y)\) and \(\varphi (\lambda )=0\).

References

  1. Axelsen, H.B., Glück, R.: What do reversible programs compute? In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 42–56. Springer, Heidelberg (2011)

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  2. Buntrock, G., Otto, F.: Growing context-sensitive languages and Church-Rosser languages. Inform. Comput. 141(1), 1–36 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  4. Li, M., Vitányi, P.M.B.: An Introduction to Kolmogorov Complexity and Its Applications. Springer, New York (1993)

    Book  MATH  Google Scholar 

  5. McNaughton, R., Narendran, P., Otto, F.: Church-Rosser Thue systems and formal languages. J. ACM 35(2), 324–344 (1988)

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  6. Niemann, G., Otto, F.: The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. Inform. Comput. 197(1–2), 1–21 (2005)

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Acknowledgments

The authors acknowledge partial support from COST Action IC1405 Reversible Computation. H. B. Axelsen was supported by the Danish Council for Independent Research \(\mid \) Natural Sciences under the Foundations of Reversible Computing project, and by an IC1405 STSM (short-term scientific mission) grant.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen E, Denmark

    Holger Bock Axelsen

  2. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Markus Holzer, Martin Kutrib & Andreas Malcher

Authors
  1. Holger Bock Axelsen
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  2. Markus Holzer
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  3. Martin Kutrib
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  4. Andreas Malcher
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Corresponding author

Correspondence to Holger Bock Axelsen .

Editor information

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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© 2016 Springer International Publishing Switzerland

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Axelsen, H.B., Holzer, M., Kutrib, M., Malcher, A. (2016). Reversible Shrinking Two-Pushdown Automata. 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_44

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29999-0

  • Online ISBN: 978-3-319-30000-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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