Advertisement

A Universal Turing Machine with 3 States and 9 Symbols

  • Manfred Kudlek
  • Yurii Rogozhin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2295)

Abstract

With an UTM(3,9) we present a new small universal Turing machine with 3 states and 9 symbols, improving a former result of an UTM(3,10).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Baiocchi, Three Small Universal Turing Machines. Proc. MCU’2001, ed. M. Margenstern, Yu. Rogozhin, Springer, LNCS 2055, pp. 1–10, 2001.Google Scholar
  2. 2.
    M.D. Davis and E.J. Weyuker, Computability, Complexity, and Languages. Academic Press, Inc., 1983.Google Scholar
  3. 3.
    M. Kudlek, Small deterministic Turing machines. Theoretical Computer Science, Elsevier Science B.V., vol. 168 (2), 1996, pp. 241–255.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Margenstern, Frontier between decidability and undecidability: a survey. Proc. of 2nd International Colloquium Universal Machines and Computations, vol.1, March 23–27, 1998, Metz, France, pp. 141–177.Google Scholar
  5. 5.
    M.L. Minsky, Size and structure of universal Turing machines using tag systems. Recursive Function Theory, Symp. in pure mathematics, Amer. Math. Soc., 5, 1962, pp. 229–238.Google Scholar
  6. 6.
    Gh. Păun,DNAComputing Based on Splicing: Universality Results. Proc. of 2nd International Colloquium Universal Machines and Computations, vol.1, March 23–27, 1998, Metz, France, pp. 67–91.Google Scholar
  7. 7.
    L.M. Pavlotskaya, Sufficient conditions for halting problem decidability of Turing machines. Avtomati i mashini (Problemi kibernetiki), Moskva, Nauka, 1978, vol. 33, pp. 91–118, (Russian).Google Scholar
  8. 8.
    R.M. Robinson, Minsky’s small universal Turing machine. International Journal of Mathematics, vol.2, N.5, 1991, pp. 551–562.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Yu. Rogozhin, Seven universal Turing machines. Systems and Theoretical Programming, Mat. Issled. no.69, Academiya Nauk Moldavskoi SSR, Kishinev, 1982, pp. 76–90, (Russian).Google Scholar
  10. 10.
    Yu. Rogozhin,A universal Turing machine with 10 states and 3 symbols. Izvestiya Akademii Nauk Respubliki Moldova, Matematika, 1992, N 4(10), pp. 80–82 (Russian).Google Scholar
  11. 11.
    Yu. Rogozhin, About Shannon’s problem for Turing machines. Computer Science Journal of Moldova, vol.1, no 3(3), 1993, pp. 108–111.Google Scholar
  12. 12.
    Yu. Rogozhin, Small universal Turing machines. Theoretical Computer Science, Elsevier Science B.V., vol. 168 (2), 1996, pp. 215–240.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Yu. Rogozhin,A Universal Turing Machine with 22 States and 2 Symbols. Romanian Journal of Information Science and Technology, vol. 1, N. 3, 1998, pp. 259–265.Google Scholar
  14. 14.
    C.E. Shannon, A universal Turing machine with two internal states. Automata studies, Ann. of Math. Stud. 34, Princeton, Princeton Univ.Press, 1956, pp. 157–165.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Manfred Kudlek
    • 1
  • Yurii Rogozhin
    • 2
  1. 1.Fachbereich InformatikUniversität HamburgHamburgGermany
  2. 2.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuRepublica Moldova

Personalised recommendations