Abstract
We define a new criterion which allows to separate cases when all non erasing Turing machines on {0, 1} have a decidable halting problem from cases where a universal non erasing machine can be constructed. It is the case of the number of left instructions in the machine program. In this paper we give the main ideas of the proof for both parts of the frontier result. We prove that there is a universal non-erasing Turing machine whose program has precisely 3 left instructions and that the halting problem is decidable for any non-erasing Turing machine on alphabet {0, 1}, the program of which contains at most 2 left instructions. For this latter result, we have a uniform decision algorithm.
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References
Margenstern M. Sur la frontière entre machines de Turing à arrêt décidable et machines de Turing universelles. LITP research report N°92.83 (Institut Blaise Pascal) (1992)
Margenstern M. Turing machines: on the frontier between a decidable halting problem and universality. Lecture Notes in Computer Science, 710, pp. 375–385, (1993)
Margenstern M. Décidabilité du problème de l'arrêt pour les machines de Turing non-effaçante sur {0, 1} et à deux instructions gauches. LITP research report N°94.03 (Institut Blaise Pascal) (1994)
Margenstern M. Une machine de Turing universelle sur {0, 1}, non-effaçante et à trois instructions gauches. LITP research report N°94.08 (Institut Blaise Pascal) (1994)
Margenstern M. Une machine de Turing universelle non-effaçante à exactement trois instructions gauches. (note to appear in CRAS, Paris)
Minsky M.L. Computation: Finite and Infinite Machines. Prentice Hall, Englewood Cliffs, N.J. (1967)
Павлоцкая Л.М. Разрешимостя проблемы остановки для некоторых классов машин Тяуринга. Математические Заметки, 13, (6), 899–909, Иуня 1973 899–909. (transl. Solvability of the halting problem for certain classes of Turing machines, Notes of the Acad. Sci. USSR, 13 (6) Nov.1973, 537–541)
Павлоцкая Л.М. О минималяном числе различных кодов вершин в граφе универсаляной машины Тяуринга. Дискретный анализ, Сборник трудов института математики CO AH CCCP, 27, 52–60, 1975. (On the minimal number of distinct codes for the vertices of the graph of a universal Turing machine, in Russian)
Рогожин Ю.В. Семя универсаляных машин Тяуринга. Математические Исследования, 69, 76–90, 1982 (Seven universal Turing machines) (in Russian)
Рогожин Ю.В. Универсаляная машина Тяуринга с 10 состояниями и 3 символами. Известия АН РМ Математика, 4 (10), 80–82, 1992 (A universal Turing machine with 10 states and 3 symbols) (in Russian)
Shannon C.E. A universal Turing machine with two internal states. Ann. of Math. Studies, 34, 157–165, (1956)
Turing A.M. On computable real numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc, ser. 2, 42, 230–265 (1936)
Wang H. Tag Systems and Lag Systems, Math. Annalen, 152, 65–74, (1963)
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Margenstern, M. (1995). Non-erasing turing machines: A new frontier between a decidable halting problem and universality. In: Baeza-Yates, R., Goles, E., Poblete, P.V. (eds) LATIN '95: Theoretical Informatics. LATIN 1995. Lecture Notes in Computer Science, vol 911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59175-3_104
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DOI: https://doi.org/10.1007/3-540-59175-3_104
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