Advertisement

Nondeterminism Is Essential in Small 2FAs with Few Reversals

  • Christos A. Kapoutsis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)

Abstract

On every n-long input, every two-way finite automaton (2fa) can reverse its head O(n) times before halting. A 2FA with few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that requires Ω(2 h ) states on every deterministic 2FA with few reversals, but only h states on a nondeterministic 2FA with few reversals.

Keywords

Hard Instance Generic String Logarithmic Space Tight Lower Bound Input Head 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berman, P., Lingas, A.: On complexity of regular languages in terms of finite automata. Report 304, Institute of Computer Science, Polish Academy of Sciences, Warsaw (1977)Google Scholar
  2. 2.
    Geffert, V., Mereghetti, C., Pighizzini, G.: Converting two-way nondeterministic unary automata into simpler automata. Theoretical Computer Science 295, 189–203 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Geffert, V., Pighizzini, G.: Two-way unary automata versus logarithmic space. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 197–208. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Hromkovič, J.: Descriptional complexity of finite automata: concepts and open problems. Journal of Automata, Languages and Combinatorics 7(4), 519–531 (2002)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Hromkovič, J., Schnitger, G.: Nondeterminism versus determinism for two-way finite automata: generalizations of Sipser’s separation. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 439–451. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Kapoutsis, C.: Small sweeping 2NFAs are not closed under complement. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 144–156. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Kapoutsis, C.: Deterministic moles cannot solve liveness. Journal of Automata, Languages and Combinatorics 12(1-2), 215–235 (2007)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Kapoutsis, C.: Two-way automata versus logarithmic space. In: Proceedings of Computer Science in Russia, pp. 359–372 (2011)Google Scholar
  9. 9.
    Leung, H.: Tight lower bounds on the size of sweeping automata. Journal of Computer and System Sciences 63(3), 384–393 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two-way finite automata. In: Proceedings of the 10th Annual ACM Symposium on Theory of Computing, May 1-3, pp. 275–286. ACM, San Diego (1978)Google Scholar
  11. 11.
    Seiferas, J.I.: Untitled manuscript, communicated to M. Sipser (October 1973)Google Scholar
  12. 12.
    Sipser, M.: Lower bounds on the size of sweeping automata. Journal of Computer and System Sciences 21(2), 195–202 (1980)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christos A. Kapoutsis
    • 1
  1. 1.LIAFA – Université Paris VIIFrance

Personalised recommendations