Tally languages accepted by Monte Carlo pushdown automata

  • Jānis Kaņeps
  • Dainis Geidmanis
  • Rūsiņš Freivalds
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1269)


Rather often difficult (and sometimes even undecidable) problems become easily decidable for tally languages, i.e. for languages in a single-letter alphabet. For instance, the class of languages recognizable by 1-way nondeterministic pushdown automata equals the class of the context-free languages, but the class of the tally languages recognizable by 1-way nondeterministic pushdown automata, contains only regular languages [LP81]. We prove that languages over one-letter alphabet accepted by randomized one-way 1-tape Monte Carlo pushdown automata are regular. However Monte Carlo pushdown automata can be much more concise than deterministic 1-way finite state automata.


Turing Machine Regular Language Finite Automaton Input Word Deterministic Finite Automaton 
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  1. [Am96]
    A.AMBAINIS, The complexity of probabilistic versus deterministic finite automata. Lecture Notes in Computer Science, 1178(1996).Google Scholar
  2. [Fr75]
    R. FREIVALDS, Fast computation by probabilistic Turing machines. Proceedings of Latvian State University, 233 (1975), 201–205 (in Russian).Google Scholar
  3. [Fr79]
    R. FREIVALDS, Fast probabilistic algorithms. Lecture Notes in Computer Science, 74 (1979), 57–69.Google Scholar
  4. [Fr81]
    R. FREIVALDS, Projections of languages recognizable by probabilistic and alternating finite multitape automata. Information Processing Letters, V. 13, 1981, 195–198.Google Scholar
  5. [Fr81a]
    R.FREIVALDS, Capabilities of different models of 1-way probabilistic automata. Izvestija VUZ, Matematika, No.5 (228), 1981, 26–34 (in Russian).Google Scholar
  6. [Fr81b]
    R. FREIVALDS, Probabilistic two-way machines. Lecture Notes in Computer Science, 118(1981), 33–45.Google Scholar
  7. [Fr82]
    R. FREIVALDS, On the growth of the number of states in result of determinization of probabilistic finite automata, Avtomatika i Vičislitelnaja Tehnika, 1982, N.3, 39–42 (in Russian)Google Scholar
  8. [Fr85]
    R. FREIVALDS, Space and reversal complexity of probabilistic one-way Turing machines. Annals of Discrete Mathematics, 24 (1985), 39–50.Google Scholar
  9. [FK94]
    R. FREIVALDS, M. KARPINSKI, Lower space bounds for randomized computation. Lecture Notes in Computer Science, 820 (1994), 580–592.Google Scholar
  10. [GM79]
    N. Z. GABBASOV, T. A. MURTAZINA, Improving the estimate of Rabin's reduction theorem, Algorithms and Automata, Kazan University, 1979, 7–10 (in Russian)Google Scholar
  11. [GJ79]
    M.R. GAREY, D.S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco, 1979.Google Scholar
  12. [Ge88]
    D. GEIDMANIS, On the capabilities of alternating and nondeterministic multitape automata. Proc. Found. of Comp. Theory, LNCS 278, Springer, Berlin, 1988, 150–154.Google Scholar
  13. [Hr85]
    J. HROMKOVIČ, On the power of alternation in automata theory. Journ. of Comp.and System Sci., Vol. 31, No. 1, 1985, 28–39Google Scholar
  14. [HI68]
    M.A. HARRISON and O.H. IBARRA, Multi-tape and multi-head pushdown automata. Information and Control, 13, 1968, 433–470.Google Scholar
  15. [Ka91]
    J. KAŅEPS, Regularity of one-letter languages acceptable by 2-way finite probabilistic automata. LNCS 529, Springer, Berlin, 1991, 287–296.Google Scholar
  16. [Ka89]
    J. KAŅEPS, Stochasticity of languages recognized by two-way finite probabilistic automata. Diskretnaya matematika, 1 (1989), 63–77 (Russian).Google Scholar
  17. [Ka91]
    J. KAŅEPS, Regularity of one-letter languages acceptable by 2-way finite probabilistic automata. Lecture Notes in Computer Science, 529 (1991), 287–296.Google Scholar
  18. [KF90]
    J. KAŅEPS, R. FREIVALDS, Minimal nontrivial apace complexity of probabilistic one-way Turing machines. LNCS, Springer, 452 1990, 355–361.Google Scholar
  19. [KV87]
    M. KARPINSKI, R. VERBEEK, On the Monte Carlo space constructible functions and separation results for probabilistic complexity classes. Information and Computation, 75 (1987), 178–189.Google Scholar
  20. [KS60]
    J.G.KEMENY, J.L.SNELL, Finite Markov Chains. Van Nostrand, 1960.Google Scholar
  21. [KSK76]
    J.G.KEMENY, J.L.SNELL, A.W.KNAPP, Denumerable Markov Chains. Springer-Verlag, 1976.Google Scholar
  22. [Ki81]
    K.N. KING, Alternating multihead finite automata. LNCS 115, Springer, Berlin, 1981, 506–520.Google Scholar
  23. [LLS78]
    R.E.LADNER, R.J.LIPTON, and L.J.STOCKMEYER, Alternating push-down automata. Conf. Rec. IEEE 19th Ann. Symp. on Found. of Comp. Sci. (1978), 92–106.Google Scholar
  24. [LP81]
    H.R.LEWIS, and CH.H.PAPADIMITRIOU, Elements of the Theory of Computation. Prentice-Hall, 1981, 466 pages.Google Scholar
  25. [NH68]
    M. NASU and N. HONDA, Fuzzy events realized by finite probabilistic automata. Information and Control, 12, 1968, 284–303.Google Scholar
  26. [Pap94]
    CH.H.PAPADIMITRIOU, Computational Complexity. Addison-Wesley, 1994.Google Scholar
  27. [Paz66]
    A. PAZ, Some aspects of probabilistic automata, Information and Control, 9(1966)Google Scholar
  28. [Ra63]
    M. O. RABIN, Probabilistic automata, Information and Control, 6(1963), 230–245.Google Scholar
  29. [Sh56]
    J.C. SHEPHERDSON, The reduction of two-way automata to one-way automata. IBM Journal of Research and Development, 3(1959), 198–200.Google Scholar
  30. [TB73]
    B. A. TRAKHTENBROT, Y. M. BARZDIN, Finite Automata: Behaviour and Synthesis. North-Holland, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Jānis Kaņeps
    • 1
  • Dainis Geidmanis
    • 1
  • Rūsiņš Freivalds
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

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