Advertisement

On Stateless Multihead Automata: Hierarchies and the Emptiness Problem

  • Oscar H. Ibarra
  • Juhani Karhumäki
  • Alexander Okhotin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)

Abstract

We look at stateless multihead finite automata in their two-way and one-way, deterministic and nondeterministic variations. The transition of a k-head automaton depends solely on the symbols currently scanned by its k heads, and every such transition moves each head one cell left or right, or instructs it to stay. We show that stateless (k + 4)-head two-way automata are more powerful than stateless k-head two-way automata. In the one-way case, we prove a tighter result: stateless (k + 1)-head one-way automata are more powerful than stateless k-head one-way automata. Finally, we show that the emptiness problem for stateless 2-head two-way automata is undecidable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Domaratzki, M.: Personal communication (August 2007)Google Scholar
  2. 2.
    Monien, B.: Two-way multihead automata over a one-letter alphabet. RAIRO Informatique theoretique 14(1), 67–82 (1980)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Păun, G.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Păun, G.: Membrane Computing, An Introduction. Springer, Heidelberg (2002)Google Scholar
  5. 5.
    Rosenberg, A.L.: On multi-head finite automata. IBM Journal of Research and Development 10(5), 388–394 (1966)zbMATHGoogle Scholar
  6. 6.
    Yang, L., Dang, Z., Ibarra, O.H.: Bond computing systems: a biologically inspired and high-level dynamics model for pervasive computing. In: Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T. (eds.) UC 2007. LNCS, vol. 4618, pp. 226–241. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Yang, L., Dang, Z., Ibarra, O.H.: On stateless automata and P systems. In: Pre-Proceedings of Workshop on Automata for Cellular and Molecular Computing (August 2007)Google Scholar
  8. 8.
    Yao, A.C., Rivest, R.L.: k + 1 heads are better than k. Journal of the ACM 25(2), 337–340 (1978)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Juhani Karhumäki
    • 2
  • Alexander Okhotin
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Academy of Finland 

Personalised recommendations