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Visit-Bounded Stack Automata

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Developments in Language Theory (DLT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13257))

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Abstract

An automaton is k-visit-bounded if during any computation its work tape head visits each tape cell at most k times. In this paper we consider stack automata which are k-visit-bounded for some integer k. This restriction resets the visits when popping (unlike similarly defined Turing machine restrictions) which we show allows the model to accept a proper superset of context-free languages and also a proper superset of languages of visit-bounded Turing machines. We study two variants of visit-bounded stack automata: one where only instructions that move the stack head downwards increase the number of visits of the destination cell, and another where any transition increases the number of visits. We prove that the two types of automata recognize the same languages. We then show that all languages recognized by visit-bounded stack automata are effectively semilinear, and hence are letter-equivalent to regular languages, which can be used to show other properties.

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References

  1. Ginsburg, S., Greibach, S., Harrison, M.: One-way stack automata. J. ACM 14(2), 389–418 (1967)

    Article  MathSciNet  Google Scholar 

  2. Ginsburg, S., Greibach, S., Harrison, M.: Stack automata and compiling. J. ACM 14(1), 172–201 (1967)

    Article  MathSciNet  Google Scholar 

  3. Greibach, S.: Checking automata and one-way stack languages. J. Comput. Syst. Sci. 3(2), 196–217 (1969)

    Article  MathSciNet  Google Scholar 

  4. Greibach, S.A.: One way finite visit automata. Theor. Comput. Sci. 6, 175–221 (1978)

    Article  MathSciNet  Google Scholar 

  5. Harju, T., Ibarra, O., Karhumäki, J., Salomaa, A.: Some decision problems concerning semilinearity and commutation. J. Comput. Syst. Sci. 65(2), 278–294 (2002)

    Article  MathSciNet  Google Scholar 

  6. Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley, Reading (1978)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  8. Ibarra, O., McQuillan, I.: Semilinearity of families of languages. Int. J. Found. Comput. Sci. 31(8), 1179–1198 (2020)

    Article  MathSciNet  Google Scholar 

  9. Ibarra, O.H., McQuillan, I.: On families of full trios containing counter machine languages. Theor. Comput. Sci. 799, 71–93 (2019)

    Article  MathSciNet  Google Scholar 

  10. Ibarra, O.H., McQuillan, I., Ravikumar, B.: On counting functions and slenderness of languages. Theor. Comput. Sci. 777, 356–378 (2019)

    Article  MathSciNet  Google Scholar 

  11. Joshi, A.K.: Tree adjoining grammars: how much context-sensitivity is required to provide reasonable structural descriptions? In: Natural Language Parsing, pp. 206–250. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  12. Parikh, R.: On context-free languages. J. ACM 13(4), 570–581 (1966)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada

    Jozef Jirásek & Ian McQuillan

Authors
  1. Jozef Jirásek
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  2. Ian McQuillan
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Correspondence to Jozef Jirásek .

Editor information

Editors and Affiliations

  1. University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Volker Diekert

  2. Ural Federal University, Ekaterinburg, Russia

    Mikhail Volkov

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Jirásek, J., McQuillan, I. (2022). Visit-Bounded Stack Automata. In: Diekert, V., Volkov, M. (eds) Developments in Language Theory. DLT 2022. Lecture Notes in Computer Science, vol 13257. Springer, Cham. https://doi.org/10.1007/978-3-031-05578-2_15

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  • DOI: https://doi.org/10.1007/978-3-031-05578-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-05577-5

  • Online ISBN: 978-3-031-05578-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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