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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boudol, G., Castellani, I.: Concurrency and atomicity. Theoret. Comput. Sci. 59 (1988) 25–34.
Corneil, D.G., Lerchs, H., Burlinham, L.S.: Complement reducible graphs. Discr. Appl. Math. 3 (1981) 163–174.
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.
Engelfriet, J., Harju, T., Proskurowski, A., Rozenberg, G.: Characterization and complexity of uniformly nonprimitive labeled 2-structures. Theoret. Comput. Sci. 154 (1996) 247–282.
Ehrenfeucht, A., ten Pas, P., Rozenberg, G.: Combinatorial properties of texts. Theor. Inf. Appl. 27 (1993) 433–464.
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.
Ehrenfeucht, A., Rozenberg, G.: Angular 2-structures. Theoret. Comput. Sci. 92 (1992) 227–248.
Ehrenfeucht, A., Rozenberg, G.: T-structures, T-functions and texts. Theoret. Comput. Sci. 116 (1993) 227–290.
Ésik, Z.: Free algebras for generalized automata and language theory. RIMS Kokyuroku 1166, Kyoto University, Kyoto (2000) 52–58.
Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984).
Giammarresi, D., Restivo, A.: Two-dimensional finite state recognizability. Fund. Inform. 25 (1996) 399–422.
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.
Grabowski, J.: On partial languages. Fund. Inform. 4 (1981) 427–498.
Hashiguchi, K., Ichihara, S., Jimbo, S.: Formal languages over free binoids. J. Autom. Lang. Comb. 5 (2000) 219–234.
Hoogeboom, H.J., ten Pas, P.: Text languages in an algebraic framework. Fund. Inform. 25 (1996) 353–380.
Hoogeboom, H.J., ten Pas, P.: Monadic second-order definable text languages. Theory Comput. Syst. 30 (1997) 335–354.
Kuske, D.: Infinite series-parallel posets: logic and languages. In: proc. ICALP 2000, LNCS, Vol. 1853. Springer (2001) 648–662.
Kuske, D.: Towards a language theory for infinite N-free pomsets. (to appear).
Lodaya, K., Weil, P.: Kleene iteration for parallelism. In: proc. FST & TCS 98, LNCS, Vol. 1530. Springer-Verlag (1998) 355–366.
Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theoret. Comput. Sci. 237 (2000) 347–380.
Lodaya, K., Weil, P.: Rationality in algebras with series operation. Inform. and Comput. (to appear).
Pin, J.-E.: Varieties of Formal Languages. Plenum Publishing Corp., NewYork (1986).
Steinby, M.: General varieties of tree languages. Theoret. Comput. Sci. 205 (1998) 1–43.
Straubing, H.: Automata, Formal Logic and Circuit Complexity. Birkhauser, Boston (1994).
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series-parallel digraphs. SIAM J. Comput. 11 (1982) 298–313.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-46011-X_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43453-5
Online ISBN: 978-3-540-46011-4
eBook Packages: Springer Book Archive