Input-Driven Multi-counter Automata

  • Martin KutribEmail author
  • Andreas Malcher
  • Matthias Wendlandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11601)


The model of deterministic input-driven multi-counter automata is introduced and studied. On such devices, the input letters uniquely determine the operations on the underlying data structure that is consisting of multiple counters. We study the computational power of the resulting language families and compare them with known language families inside the Chomsky hierarchy. In addition, it is possible to prove a proper counter hierarchy depending on the alphabet size. This means that any input alphabet induces an upper bound which depends on the alphabet size only, such that \(k+1\) counters are more powerful than k counters as long as k is less than this bound. The hierarchy interestingly collapses at the level of the bound. Furthermore, we investigate the closure properties of the language families. Finally, the undecidability of the emptiness problem is derived for input-driven two-counter automata.


  1. 1.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: Babai, L. (ed.) STOC 2004, pp. 202–211. ACM (2004).
  2. 2.
    Bárány, V., Löding, C., Serre, O.: Regularity problems for visibly pushdown languages. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 420–431. Springer, Heidelberg (2006). Scholar
  3. 3.
    Bensch, S., Holzer, M., Kutrib, M., Malcher, A.: Input-driven stack automata. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds.) TCS 2012. LNCS, vol. 7604, pp. 28–42. Springer, Heidelberg (2012). Scholar
  4. 4.
    Böhm, S., Göller, S., Jančar, P.: Equivalence of deterministic one-counter automata is NL-complete. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) STOC 2013, pp. 131–140. ACM (2013).
  5. 5.
    von Braunmühl, B., Verbeek, R.: Input-driven languages are recognized in \(\log n\) space. In: Topics in the Theory of Computation, Mathematics Studies, vol. 102, pp. 1–19, North-Holland (1985). Scholar
  6. 6.
    Breveglieri, L., Cherubini, A., Citrini, C., Crespi-Reghizzi, S.: Multi-push-down languages and grammars. Int. J. Found. Comput. Sci. 7, 253–292 (1996). Scholar
  7. 7.
    Fischer, P.C., Meyer, A.R., Rosenberg, A.L.: Counter machines and counter languages. Math. Syst. Theory 2, 265–283 (1968). Scholar
  8. 8.
    Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theor. Comput. Sci. 7, 311–324 (1978). Scholar
  9. 9.
    Hahn, M., Krebs, A., Lange, K.-J., Ludwig, M.: Visibly counter languages and the structure of \(\rm NC^{1}\). In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9235, pp. 384–394. Springer, Heidelberg (2015). Scholar
  10. 10.
    Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25, 116–133 (1978). Scholar
  11. 11.
    Ibarra, O.H.: Visibly pushdown automata and transducers with counters. Fund. Inform. 148, 291–308 (2016). Scholar
  12. 12.
    Krebs, A., Lange, K., Ludwig, M.: Visibly counter languages and constant depth circuits. In: Mayr, E.W., Ollinger, N. (eds.) STACS 2015. LIPIcs, vol. 30, pp. 594–607 (2015).
  13. 13.
    Kutrib, M., Malcher, A., Mereghetti, C., Palano, B., Wendlandt, M.: Deterministic input-driven queue automata: finite turns, decidability, and closure properties. Theor. Comput. Sci. 578, 58–71 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kutrib, M., Malcher, A., Wendlandt, M.: Tinput-driven pushdown, counter, and stack automata. Fund. Inform. 155, 59–88 (2017). Scholar
  15. 15.
    La Torre, S., Napoli, M., Parlato, G.: Scope-bounded pushdown languages. Int. J. Found. Comput. Sci. 27, 215–234 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. In: de Bakker, J., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980). Scholar
  17. 17.
    Minsky, M.L.: Recursive unsolvability of Post’s problem of “tag” and other topics in theory of Turing machines. Ann. Math. 74, 437–455 (1961). 2nd SMathSciNetCrossRefGoogle Scholar
  18. 18.
    Okhotin, A., Salomaa, K.: Complexity of input-driven pushdown automata. SIGACT News 45, 47–67 (2014). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Martin Kutrib
    • 1
    Email author
  • Andreas Malcher
    • 1
  • Matthias Wendlandt
    • 1
  1. 1.Institut für InformatikUniversität GiessenGiessenGermany

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