Solvability of the halting problem for certain classes of Turing machines

  • L. M. Pavlotskaya


One method of proving that some Turing machine is not universal is to prove that the halting problem is solvable for it. Therefore, to obtain a lower bound on the complexity of a universal machine, it is convenient to have a criterion of solvability of the halting problem. In the present paper, we establish some of these criteria; they are formulated in terms of properties of machine graphs and computations.


Turing Machine Universal Machine Machine Graph 
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Literature cited

  1. 1.
    C. E. Shannon, “A universal Turing machine with two internal states,” in: Automata Studies (C. E. Shannon and J. McCarthy, editors), Princeton University Press, Princeton (1956).Google Scholar
  2. 2.
    M. L. Minsky, “Size and structure of universal Turing machines using tag systems,” in: Recursive Function Theory, Symposia in Pure Mathematics, Amer. Math. Soc.,5 (1962).Google Scholar
  3. 3.
    M. L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, Inc., Englewood Cliffs, N. J. (1967).Google Scholar
  4. 4.
    Yu. A. Kryukov, “Turing machines with two symbols and two states,” Algebra i Logika,6, No. 3, 54–60 (1967).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • L. M. Pavlotskaya
    • 1
  1. 1.Moscow Energy InstituteUSSR

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