How to Synchronize the Heads of a Multitape Automaton

  • Oscar H. Ibarra
  • Nicholas Q. Tran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)


Given an n-tape automaton M with a one-way read-only head per tape and a right end marker $ on each tape, we say that M is aligned or 0-synchronized (or simply, synchronized) if for every n-tuple x = (x 1, …, x n ) that is accepted, there is a computation on x such that at any time during the computation, all heads, except those that have reached the end marker, are on the same position. When a head reaches the marker, it can no longer move. As usual, an n-tuple x = (x 1, …, x n ) is accepted if M eventually reaches the configuration where all n heads are on $ in an accepting state. In two recent papers, we looked at the problem of deciding, given an n-tape automaton of a given type, whether there exists an equivalent synchronized n-tape automaton of the same type. In this paper, we exhibit various classes of multitape automata which can(not) be converted to equivalent synchronized multitape automata.


multitape automata aligned synchronized semilinear decidable undecidable 1-reversal counters reversal-bounded counters 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baker, B.S., Book, R.V.: Reversal-bounded multipushdown machines. J. Computer and System Sciences 8, 315–332 (1974)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Eğecioğlu, Ö., Ibarra, O.H., Tran, N.Q.: Multitape NFA: Weak Synchronization of the Input Heads. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 238–250. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Ginsburg, G., Spanier, E.: Bounded Algol-like languages. Trans. of the Amer. Math. Society 113, 333–368 (1964)MathSciNetMATHGoogle Scholar
  4. 4.
    Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. Assoc. Comput. Math. 25, 116–133 (1978)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Ibarra, O.H., Seki, S.: Characterizations of bounded semilinear languages by one-way and two-way deterministic machines. In: Proc. 13th Int. Conf. on Automata and Formal Languages, AFL 2011 (2011)Google Scholar
  6. 6.
    Ibarra, O.H., Tran, N.Q.: Weak Synchronization and Synchronizability of Multitape Pushdown Automata and Turing Machines. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 337–350. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Minsky, M.: Recursive unsolvability of Post’s problem of Tag and other topics in the theory of Turing machines. Ann. of Math. (74), 437–455 (1961)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Parikh, R.J.: On context-free languages. J. Assoc. Comput. Mach. 13, 570–581 (1966)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Yu, F., Bultan, T., Ibarra, O.H.: Relational String Verification Using Multi-track Automata. In: Domaratzki, M., Salomaa, K. (eds.) CIAA 2010. LNCS, vol. 6482, pp. 290–299. Springer, Heidelberg (2011); Extended version in International J. Found. of Comput. Sci. 22, 1909–1924 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Nicholas Q. Tran
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Mathematics & Computer ScienceSanta Clara UniversitySanta ClaraUSA

Personalised recommendations