Solvability of the halting problem for certain classes of Turing machines
- 78 Downloads
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.
KeywordsTuring Machine Universal Machine Machine Graph
Unable to display preview. Download preview PDF.
- 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.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.M. L. Minsky, Computation: Finite and Infinite Machines, Prentice-Hall, Inc., Englewood Cliffs, N. J. (1967).Google Scholar
- 4.Yu. A. Kryukov, “Turing machines with two symbols and two states,” Algebra i Logika,6, No. 3, 54–60 (1967).Google Scholar