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Tree-stack automata

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Abstract

We introduce a new model of stack automata, the “tree-stack automata,” extending the linear stack to a tree-stack. A main subject of our investigations is to explore the relationship between tree-stack automata and stack automata. The main result of this paper is that tree-stack have the same recognition power as stack-pushdown automata, another (well-known) extension of stack automata. Therefore we obtain that the class of languages accepted by the one-way (linear) stack automata is a proper subset of the class of languages accepted by the one-way tree-stack automata and that two-way tree-stack automata have the same recognition power as two-way (linear) stack automata. As a special case of tree-stack automata we consider tree-pushdown automata. As opposed to stack automata the tree-pushdown storage does not extend the recognition power of one-way (resp. two-way) pushdown automata.

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References

  1. Aho, A. V. (1969), Nested stack automata,J. Assoc. Comput. Mach. 16, 383–406.

    MathSciNet  MATH  Google Scholar 

  2. Beeri, C. (1975), Two-way nested stack automata are equivalent to two-way stack automata,J. Comput. System Sci. 10, 317–339.

    MathSciNet  MATH  Google Scholar 

  3. Brainerd, W. S. (1969), Tree generating regular systems,Inform. and Control 14, 217–231.

    Article  MathSciNet  MATH  Google Scholar 

  4. Büchi, J. R. (1960), Regular canonical systems,Archiv Math. Logik Grundlag. 6, 91–111.

    Google Scholar 

  5. Damm, W. (1982), The IO and OI hierarchies,Theoret. Comput. Sci. 20, 95–207.

    Article  MathSciNet  MATH  Google Scholar 

  6. Engelfriet, J. (1991), Iterated stack automata and complexity classes,Inform. and Comput. 95, 21–75.

    Article  MathSciNet  Google Scholar 

  7. Engelfriet, J., Meineche Schmidt, E., and van Leeuwen, J. (1980), Stack machines and classes of nonnested macro languages,J. Assoc. Comput. Mach. 27, 96–117.

    MathSciNet  MATH  Google Scholar 

  8. Engelfriet, J., Rozenberg, G., and Slutzki, G. (1980), Tree transducers, L systems, and two-way machines,J. Comput. System Sci. 20, 150–202.

    Article  MathSciNet  MATH  Google Scholar 

  9. Engelfriet, J., and Vogler, H. (1986), Pushdown machines for the macro tree transducer,Theoret. Comput. Sci. 42, 251–368.

    Article  MathSciNet  MATH  Google Scholar 

  10. Engelfriet, J., and Vogler, H. (1988), High-level tree transducers and iterated pushdown tree transducer,Acta Inform. 26, 131–192.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ginsburg, S., Greibach, S. A., and Harrison, M. A. (1967), Stack automata and compiling,J. Assoc. Comput. Mach. 14, 172–201.

    MathSciNet  MATH  Google Scholar 

  12. Ginsburg, S., Greibach, S. A., and Harrison, M. A. (1967), One-way stack automata,J. Assoc. Comput. Mach. 14, 389–418.

    MathSciNet  MATH  Google Scholar 

  13. Greibach, S. A. (1969), Checking automata and one-way stack languages,J. Comput. System Sci. 3, 196–217.

    MathSciNet  MATH  Google Scholar 

  14. Guessarian, I. (1983), Pushdown tree automata,Math. Systems Theory 16, 237–263.

    Article  MathSciNet  MATH  Google Scholar 

  15. Harrison, M. A., and Schkolnick, M. (1971), A grammatical characterization of one-way nondeterministic stack languages,J. Assoc. Comput. Mach. 18, 148–172.

    MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  17. Langmaack, H. (1973), On correct procedure parameter transmission in higher programming languages,Acta Inform. 2, 110–142.

    MathSciNet  MATH  Google Scholar 

  18. Langmaack, H. (1973), On procedures as open subroutines, I,Acta Inform. 2, 331–333.

    Google Scholar 

  19. Langmaack, H. (1974), On procedures as open subroutines, II,Acta Inform. 3, 227–241.

    Article  MathSciNet  MATH  Google Scholar 

  20. Lippe, W.-M. (1976), Über die Entscheidbarkeit der formalen Erreichbarkeit von Prozeduren bei monadischen Programmen, 4.Fachtagung über Programmiersprachen, Informatik-Fachberichte 1, Springer-Verlag, Berlin, pp. 124–134.

    Google Scholar 

  21. Lippe, W.-M., (1980), Erweiterungen von Dendrogrammatiken,J. Inform. Process. Cybernet. 16, 21–39.

    MathSciNet  MATH  Google Scholar 

  22. Lippe, W.-M., (1983), Top-Down-Baumerzeugende Systeme und Automaten, Habilitation Thesis, University Kiel.

  23. Ogden, W. F., (1969), Intercalation theorems for stack languages,Proc. ACM Symp. on Theory of Computing, Marina del Rey, CA, pp. 31–42.

    Chapter  Google Scholar 

  24. Rounds, W. C. (1970), Mappings and grammars on trees,Math. Systems Theory 4, 257–287.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Fachbereich 15, Institut für Numerische und Instrumentelle Mathematik/Informatik, Wilhelms-Universität Münster, Einsteinstrasse 62, D-48149, Münster, Germany

    W. Golubski & W. M. Lippe

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  1. W. Golubski
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  2. W. M. Lippe
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Golubski, W., Lippe, W.M. Tree-stack automata. Math. Systems Theory 29, 227–244 (1996). https://doi.org/10.1007/BF01201277

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  • DOI: https://doi.org/10.1007/BF01201277

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