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Automata on Series-Parallel Biposets

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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

We provide the basics of a 2-dimensional theory of automata on seriesparallel biposets. We define recognizable, regular and rational sets of seriesparallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

Research supported by grant no. T30511 from the National Foundation of Hungary for Scientific Research.

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References

  1. Boudol, G., Castellani, I.: Concurrency and atomicity. Theoret. Comput. Sci. 59 (1988) 25–34.

    Article  MathSciNet  MATH  Google Scholar 

  2. Corneil, D.G., Lerchs, H., Burlinham, L.S.: Complement reducible graphs. Discr. Appl. Math. 3 (1981) 163–174.

    Article  MATH  Google Scholar 

  3. Courcelle, B.: The monadic second-order logic on graphs V: on closing the gap between definability and recognizability. Theoret. Comput. Sci. 80 (1991) 153–202.

    Article  MATH  MathSciNet  Google Scholar 

  4. Engelfriet, J., Harju, T., Proskurowski, A., Rozenberg, G.: Characterization and complexity of uniformly nonprimitive labeled 2-structures. Theoret. Comput. Sci. 154 (1996) 247–282.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ehrenfeucht, A., ten Pas, P., Rozenberg, G.: Combinatorial properties of texts. Theor. Inf. Appl. 27 (1993) 433–464.

    MATH  Google Scholar 

  6. Ehrenfeucht, A., Rozenberg, G.: Theory of 2-structures, Part 1: clans, basic subclasses, and morphisms. Part 2: representation through labeled tree families. Theoret. Comput. Sci. 70 (1990) 277–303, 305–342.

    Article  MATH  MathSciNet  Google Scholar 

  7. Ehrenfeucht, A., Rozenberg, G.: Angular 2-structures. Theoret. Comput. Sci. 92 (1992) 227–248.

    Article  MATH  MathSciNet  Google Scholar 

  8. Ehrenfeucht, A., Rozenberg, G.: T-structures, T-functions and texts. Theoret. Comput. Sci. 116 (1993) 227–290.

    Article  MATH  MathSciNet  Google Scholar 

  9. Ésik, Z.: Free algebras for generalized automata and language theory. RIMS Kokyuroku 1166, Kyoto University, Kyoto (2000) 52–58.

    Google Scholar 

  10. Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984).

    MATH  Google Scholar 

  11. Giammarresi, D., Restivo, A.: Two-dimensional finite state recognizability. Fund. Inform. 25 (1996) 399–422.

    MATH  MathSciNet  Google Scholar 

  12. Giammarresi, D., Restivo, A., Seibert, S., Thomas, W.: Monadic second order logic over pictures and recognizability by tiling systems. In: proc. STACS 94, Caen, LNCS, Vol. 775. Springer (1994) 365–375.

    Google Scholar 

  13. Grabowski, J.: On partial languages. Fund. Inform. 4 (1981) 427–498.

    MATH  MathSciNet  Google Scholar 

  14. Hashiguchi, K., Ichihara, S., Jimbo, S.: Formal languages over free binoids. J. Autom. Lang. Comb. 5 (2000) 219–234.

    MATH  MathSciNet  Google Scholar 

  15. Hoogeboom, H.J., ten Pas, P.: Text languages in an algebraic framework. Fund. Inform. 25 (1996) 353–380.

    MATH  MathSciNet  Google Scholar 

  16. Hoogeboom, H.J., ten Pas, P.: Monadic second-order definable text languages. Theory Comput. Syst. 30 (1997) 335–354.

    Article  MATH  MathSciNet  Google Scholar 

  17. Kuske, D.: Infinite series-parallel posets: logic and languages. In: proc. ICALP 2000, LNCS, Vol. 1853. Springer (2001) 648–662.

    Google Scholar 

  18. Kuske, D.: Towards a language theory for infinite N-free pomsets. (to appear).

    Google Scholar 

  19. Lodaya, K., Weil, P.: Kleene iteration for parallelism. In: proc. FST & TCS 98, LNCS, Vol. 1530. Springer-Verlag (1998) 355–366.

    Google Scholar 

  20. Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theoret. Comput. Sci. 237 (2000) 347–380.

    Article  MATH  MathSciNet  Google Scholar 

  21. Lodaya, K., Weil, P.: Rationality in algebras with series operation. Inform. and Comput. (to appear).

    Google Scholar 

  22. Pin, J.-E.: Varieties of Formal Languages. Plenum Publishing Corp., NewYork (1986).

    MATH  Google Scholar 

  23. Steinby, M.: General varieties of tree languages. Theoret. Comput. Sci. 205 (1998) 1–43.

    Article  MATH  MathSciNet  Google Scholar 

  24. Straubing, H.: Automata, Formal Logic and Circuit Complexity. Birkhauser, Boston (1994).

    MATH  Google Scholar 

  25. Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series-parallel digraphs. SIAM J. Comput. 11 (1982) 298–313.

    Article  MATH  MathSciNet  Google Scholar 

  26. Wilke, Th.: Star-free picture expressions are strictly weaker than first-order logic. In: proc. ICALP 97, LNCS, Vol. 1256. Springer-Verlag (1997) 347–357.

    Google Scholar 

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Ésik, Z., Németh, Z.L. (2002). Automata on Series-Parallel Biposets. 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_18

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  • DOI: https://doi.org/10.1007/3-540-46011-X_18

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  • Print ISBN: 978-3-540-43453-5

  • Online ISBN: 978-3-540-46011-4

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