On the Size Complexity of Rotating and Sweeping Automata

  • Christos Kapoutsis
  • Richard Královič
  • Tobias Mömke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5257)


We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas). Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset on the left end of the input every time the right endmarker is read. We introduce a list of language operators and study the corresponding closure properties of the size complexity classes defined by these automata. Our conclusions reveal the logical structure of certain proofs of known separations in the hierarchy of these classes and allow us to systematically construct alternative problems to witness these separations.


Finite Automaton Conjunctive Normal Form Closure Property Positive Instance Language Operator 
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  1. 1.
    Berman, P.: A note on sweeping automata. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 91–97. Springer, Heidelberg (1980)Google Scholar
  2. 2.
    Geffert, V., Mereghetti, C., Pighizzini, G.: Complementing two-way finite automata. Information and Computation 205(8), 1173–1187 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kapoutsis, C., Královič, R., Mömke, T.: An exponential gap between LasVegas and deterministic sweeping finite automata. In: Hromkovič, J., Královič, R., Nunkesser, M., Widmayer, P. (eds.) SAGA 2007. LNCS, vol. 4665, pp. 130–141. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Micali, S.: Two-way deterministic finite automata are exponentially more succinct than sweeping automata. Information Processing Letters 12(2), 103–105 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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, San Diego, California, USA, May 1-3, 1978. ACM, New York (1978)Google Scholar
  6. 6.
    Seiferas, J.I.: Untitled manuscript. Communicated to Michael Sipser (October 1973)Google Scholar
  7. 7.
    Sipser, M.: Lower bounds on the size of sweeping automata. Journal of Computer and System Sciences 21(2), 195–202 (1980)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Christos Kapoutsis
    • 1
  • Richard Královič
    • 1
  • Tobias Mömke
    • 1
  1. 1.Department of Computer ScienceETH Zürich 

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