Advertisement

Characterizing the Regular Languages by Nonforgetting Restarting Automata

  • Norbert Hundeshagen
  • Friedrich Otto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

We study nonforgetting R- and nonforgetting deterministic RR-automata of window size one, that is, nf-R(1)- and det-nf-RR(1)-automata. Our main result shows that the monotone variants of these two types of restarting automata characterize the regular languages. On the other hand, we prove that already the non-monotone deterministic nonforgetting R(1)-automata accept a class of languages that is incomparable to the class of semi-linear languages with respect to inclusion, but that properly includes the class of languages that are accepted by globally deterministic cooperating distributed systems of stateless deterministic R(1)-automata.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aho, A., Hopcroft, J., Ullman, J.: A general theory of translation. Math. Systems Theory 3, 193–221 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: Restarting automata. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 283–292. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  3. 3.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: On restarting automata with rewriting. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 119–136. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Jančar, P., Mráz, F., Plátek, M., Vogel, J.: On monotonic automata with a restart operation. J. Autom. Lang. Comb. 4, 287–311 (1999)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Kutrib, M., Messerschmidt, H., Otto, F.: On stateless two-pushdown automata and restarting automata. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) Proc. AFL 2008, pp. 257–268. Computer Science and Automation Research Institute, Hungarian Academy of Sciences (2008)Google Scholar
  6. 6.
    McNaughton, R., Narendran, P., Otto, F.: Church-Rosser Thue systems and formal languages. J. ACM 35, 324–344 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Messerschmidt, H., Otto, F.: Cooperating distributed systems of restarting automata. Intern. J. Found. Comp. Sci. 18, 1333–1342 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Messerschmidt, H., Otto, F.: On deterministic CD-systems of restarting automata. Intern. J. Found. Comp. Sci. 20, 185–209 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Messerschmidt, H., Otto, F.: A hierarchy of monotone deterministic nonforgetting restarting automata. Theory Comput. Syst. 48, 343–373 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Messerschmidt, H., Stamer, H.: Restart-Automaten mit mehreren Restart-Zuständen. In: Bordihn, H. (ed.) Proc. of Workshop ‘Formale Sprachen in der Linguistik’ und 14. Theorietag ‘Automaten und Formale Sprachen’, pp. 111–116. Institut für Informatik, Universität Potsdam (2004)Google Scholar
  11. 11.
    Mráz, F.: Lookahead hierarchies of restarting automata. J. Autom. Lang. Comb. 6, 493–506 (2001)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Nagy, B., Otto, F.: CD-systems of stateless deterministic R(1)-automata accept all rational trace languages. In: Dediu, A., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 463–474. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Nagy, B., Otto, F.: Globally deterministic CD-systems of stateless R(1)-automata. In: Dediu, A.-H., Inenaga, S., Martin-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 390–401. Springer, Heidelberg (2011)Google Scholar
  14. 14.
    Reimann, J.: Beschreibungskomplexität von Restart-Automaten. PhD thesis, Naturwissenschaftliche Fachbereiche, Justus-Liebig-Universität Giessen (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Norbert Hundeshagen
    • 1
  • Friedrich Otto
    • 1
  1. 1.Fachbereich Elektrotechnik/InformatikUniversität KasselKasselGermany

Personalised recommendations