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Partially-Ordered Two-Way Automata: A New Characterization of DA

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Developments in Language Theory (DLT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2295))

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Abstract

In this paper,we consider finite automata with the restriction that whenever the automaton leaves a state it never returns to it. Equivalently we may assume that the states set is partially ordered and the automaton may never move “backwards” to a smaller state. p] We show that different types of partially-ordered automata characterize different language classes between level 1 and 3/2 of the Straubing-Thérien-Hierarchy. p] In particular, we prove that partially-ordered 2-way DFAs recognize exactly the class UL of unambiguous languages introduced by Schützenberger in 1976. As shown by Schützenberger, this class coincides with the class of those languages whose syntactic monoid is in the variety DA, a specific subclass of all “groupfree” (or “aperiodic”) semigroups.DA has turned out to possess a lot of appealing characterizations. Our result adds one more to these: partially-ordered two-way automata recognize exactly those languages whose syntactic monoid is in DA.

Supported by NSERC of Canada, by FCAR du Québec, and by the Alexander-von-Humboldt-Gesellschaft.Work done while on leave at the Universität Tübingen, Germany.

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References

  1. M. Arfi. Opération polynomiales et hiérarchies de concaténation. Theoretical Computer Science, 91:71–84, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  2. J.-C. Birget. Concatenation of inputs in a two-way automaton. Theoretical Computer Science, 63:141–156, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  3. J.-C. Birget. Positional simulation of two-way automata: Proof of a conjecture of R. Kannan and generalizations. Journal of Computer and System Sciences, 45(2):154–179, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Engelfriet and H. Hoogeboom. Two-way finite state transducers and monadic second-order logic. In Proceedings 26th International Colloqium on Automata, Languages and Programming, volume 1644 of Lecture Notes in Computer Science, pages 311–320, Berlin Heidelberg, 1999. Springer Verlag.

    Google Scholar 

  5. S. Eilenberg. Automata, Languages, and Machines, volume B. Academic Press, NewYork, 1976.

    MATH  Google Scholar 

  6. N. Globerman and D. Harel. Complexity results for two-way and multi-pebble automata and their logics. Theoretical Computer Science, 169:161–184, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Hromkovic and G. Schnitger. On the power of Las Vegas II. Two-way finite automata. In Proceedings 26th International Colloqium on Automata, Languages and Programming, volume 1644 of Lecture Notes in Computer Science, pages 433–442, Berlin Heidelberg, 1999. Springer Verlag.

    Google Scholar 

  8. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley Series in Computer Science. Addison-Wesley, Reading, MA, 1979.

    Google Scholar 

  9. S. Micali. Two-way deterministic finite automata are exponentially more succinct than sweeping automata. Information Processing Letters, 12:103–105, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  10. P. McKenzie, T. Schwentick, D. Thérien, and H. Vollmer. The many faces of a translation. In Proceedings 27th International Colloqium on Automata, Languages and Programming, volume 1853 of Lecture Notes in Computer Science, pages 890–901, Berlin Heidelberg, 2000. SpringerVerlag. By a mistake of the organizers while reformatting this paper, alas, all equality signs disappeared in the proceedings version. Refer to ftp://ftp-info4.informatik.uni-wuerzburg.de/pub/TRs/mc-sc-th-vo00.ps.gz for a full version with equality signs.

    Google Scholar 

  11. J. E. Pin. Varieties of Formal Languages. Plenum Press, NewYork, 1986.

    MATH  Google Scholar 

  12. J. E. Pin. Syntactic semigroups. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume I, pages 679–746. SpringerVerlag, Berlin Heidelberg, 1997.

    Google Scholar 

  13. J.-E. Pin and P. Weil. Polynomial closure and unambiguous product. Theory of Computing Systems, 30:383–422, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Schützenberger. Sur le produit de concatenation non ambigu. Semigroup Forum, 13:47–75, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Straubing. Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Boston, 1994.

    MATH  Google Scholar 

  16. D. Thérien and T. Wilke. Over words, two variables are as powerful as one quantifier alternation: FO2 = Σ2 ∩ Π2. In Proceedings 30th Symposium on Theory of Computing, pages 234–240, NewYork, 1998. ACM Press.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032, Hans-Meerwein-Straße, Marburg, Germany

    Thomas Schwentick

  2. School of Computer Science, McGill University, 3480 University Street, H3A 2A7, Montréal (Québec), Canada

    Denis Thérien

  3. Theoretische Informatik, UniversitätWürzburg, 97074, Am Hubland, Würzburg, Germany

    Heribert Vollmer

Authors
  1. Thomas Schwentick
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  2. Denis Thérien
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  3. Heribert Vollmer
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Editor information

Editors and Affiliations

  1. Institut für Algebra und Computermathematik Abt. für Theoretische Informatik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Werner Kuich

  2. Department of Computer Science, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science, Lemminkaisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Schwentick, T., Thérien, D., Vollmer, H. (2002). Partially-Ordered Two-Way Automata: A New Characterization of DA. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_20

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  • DOI: https://doi.org/10.1007/3-540-46011-X_20

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