Revolving-Input Finite Automata

  • Henning Bordihn
  • Markus Holzer
  • Martin Kutrib
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3572)


We introduce and investigate revolving-input finite automata, which are nondeterministic finite automata with the additional ability to shift the remaining part of the input. We consider three different modes of shifting, namely revolving to the left, revolving to the right, and circular interchanging. We show that the latter operation does not increase the computational power of finite automata, even if the number of revolving operations is unbounded. The same result is obtained for the former two operations in case of an arbitrary but constant number of applications allowed. An unbounded number of these operations leads to language families that are properly contained in the family of context-sensitive languages, are incomparable with the family of context-free languages, and are strictly more powerful than regular languages. Moreover, we show that right revolving can be simulated by left revolving, when considering the mirror image of the input.


Regular Language Finite Automaton Language Family Pigeon Hole Principle Unbounded Number 
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  1. 1.
    Bordihn, H., Holzer, M., Kutrib, M.: Input reversals and iterated pushdown automata: A new characterization of khabbaz geometric hierarchy of languages. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 102–113. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Chomsky, N.: Formal Properties of Grammars. In: Handbook of Mathematic Psychology, vol. 2, pp. 323–418. Wiley & Sons, New York (1962)Google Scholar
  3. 3.
    Evey, R.J.: The Theory and Applications of Pushdown Store Machines. Ph.D thesis, Harvard University, Massachusetts (1963)Google Scholar
  4. 4.
    Ginsburg, S.: Algebraic and Automata-Theoretic Properties of Formal Languages. North-Holland, Amsterdam (1975)zbMATHGoogle Scholar
  5. 5.
    Ginsburg, S., Greibach, S.A., Harrison, M.A.: One-way stack automata. Journal of the ACM 14, 389–418 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Ginsburg, S., Spanier, E.H.: Control sets on grammars. Mathematical Systems Theory 2, 159–177 (1968)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Greibach, S.A.: An infinite hierarchy of context-free languages. Journal of the ACM 16, 91–106 (1969)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Holzer, M., Kutrib, M.: Flip-pushdown automata: k +1 pushdown reversals are better than k. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 490–501. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Khabbaz, N.A.: Control sets and linear grammars. Information and Control 25, 206–221 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Khabbaz, N.A.: A geometric hierarchy of languages. Journal of Computer and System Sciences 8, 142–157 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Sarkar, P.: Pushdown automaton with the ability to flip its stack. Report TR01-081, Electronic Colloquium on Computational Complexity, ECCC (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Markus Holzer
    • 2
  • Martin Kutrib
    • 3
  1. 1.Institut für InformatikUniversität PotsdamPotsdamGermany
  2. 2.Institut für InformatikTechnische Universität MünchenGarching bei MünchenGermany
  3. 3.Institut für InformatikUniversität GiessenGiessenGermany

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