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Turing Machines for Dummies

Why Representations Do Matter

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Book cover SOFSEM 2012: Theory and Practice of Computer Science (SOFSEM 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7147))

Abstract

Various methods exists in the litearture for denoting the configuration of a Turing Machine. A key difference is whether the head position is indicated by some integer (mathematical representation) or is specified by writing the machine state next to the scanned tape symbol (intrinsic representation).

From a mathematical perspective this will make no difference. However, since Turing Machines are primarily used for proving undecidability and/or hardness results these representations do matter. Based on a number of applications we show that the intrinsic representation should be preferred.

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References

  1. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. Assoc. Comput. Mach. 28, 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cook, S.A.: The complexity of theorem proving procedures. In: Proc. ACM Symposium Theory of Computing, vol. 3, pp. 151–158 (1971)

    Google Scholar 

  3. Chlebus, B.G.: Domino-tiling games. J. Comput. Syst. Sci. 32, 374–392 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co. (1979)

    Google Scholar 

  5. Hartmanis, J., Simon, J.: On the power of multiplication in random access machines. Proc. IEEE Switching and Automata Theory 15, 13–23 (1974)

    MathSciNet  Google Scholar 

  6. Hennie, F.C., Stearns, R.E.: Two-way simulation of multi-tape Turing machines. J. Assoc. Comput. Mach. 13, 533–546 (1966)

    Article  MATH  Google Scholar 

  7. Immerman, N.: Nondeterministic space is closed under complementation. SIAM J. Comput. 17, 935–938 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jones, J.P., Matijasevič, Y.V.: Register machine proof of the theorem on exponential Diophantine representation of enumerable sets. J. Symb. Logic 49, 818–829 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kleene, S.C.: Introduction to Metamathematics. Noth Holland Publ. Cie (1952)

    Google Scholar 

  10. Levin, L.A.: Universal’nie zadachi perebora. Problemi Peredachi Informatsie IX, 115–116 (1973) (in Russian)

    Google Scholar 

  11. Lewis, H.R.: Complexity of solvable cases of the decision problem for the predicate calculus. In: Proc. IEEE FOCS, vol. 19, pp. 35–47 (1978)

    Google Scholar 

  12. Lewis, H.R., Papadimitriou, C.H.: Elements of the Theory of Computation. Prentice-Hall (1981)

    Google Scholar 

  13. Pratt, V.R., Stockmeyer, L.J.: A characterization of the power of vector machines. J. Comput. Syst. Sci. 12, 198–221 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  14. Savelsberg, M.P.W., van Emde Boas, P.: BOUNDED TILING, an alternative to SATISFIABILITY? In: Wechsung, G. (ed.) Proc. 2nd Frege Memorial Conference, Schwerin. Mathematische Forschung, vol. 20, pp. 401–407. Akademie Verlag (September 1984)

    Google Scholar 

  15. Savitch, W.J.: Relations between Deterministic and Nondeterministic tape Complexities. J Comput. Syst. Sci. 12, 177–192 (1970)

    Article  MATH  Google Scholar 

  16. Slisenko, A.O.: A simplified proof of the real-time recognizability of palindromes on Turing Machines. J. Mathematical Sciences 5(1), 68–77 (1981)

    MATH  Google Scholar 

  17. Spaan, E., Torenvliet, L., van Emde Boas, P.: Nondeterminism, fairness and a fundamental analogy. EATCS Bulletin 37, 186–193 (1989)

    MATH  Google Scholar 

  18. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time. In: Proc. ACM STOC, vol. 5, pp. 1–9 (1973)

    Google Scholar 

  19. Stockmeyer, L.: The complexity of decision problems in automata theory and logic, Report MAC-TR-133, MIT (1974)

    Google Scholar 

  20. Szelepsényi, R.: The method of forcing for nondeterministic automata. Bull. EATCS 33, 96–100 (1987)

    Google Scholar 

  21. Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. Ser. 2 42, 230–265 (1936)

    MATH  Google Scholar 

  22. van Emde Boas, P.: Dominoes are forever. In: Priese, L. (ed.) Proc. 1st GTI Workshop, Paderborn, Rheie Theoretische Informatik UGH Paderborn, vol. 13 (1982)

    Google Scholar 

  23. van Emde Boas, P.: The second machine class 2, an encyclopedic view on the parallel computation thesis. In: Rasiowa, H. (ed.) Mathematical Problems in Computation Theory, vol. 21, pp. 235–256. Banach Center Publications (1987)

    Google Scholar 

  24. van Emde Boas, P.: Machine models and simulations. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A, pp. 3–66. North Holland Publ. Comp. (1990)

    Google Scholar 

  25. van Emde Boas, P.: The convenience of tiling. In: Sorbi, A. (ed.) Complexity, Logic and Recursion Theory. Lect. Notes in Pure and Appled Math., vol. 187, pp. 331–363 (1997)

    Google Scholar 

  26. van Emde Boas, H.: Turing Tiles, Web application located at, http://www.squaringthecircles.com/turingtiles/

  27. Vitányi, P.M.B.: An optimal simulation of counter machines. SIAM J. Comput. 14, 1–33 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. ILLC, FNWI, Universiteit van Amsterdam, P.O. Box 94242, 1090, GE, Amsterdam, USA

    Peter van Emde Boas

  2. Bronstee.com Software & Services B.V., Heemstede, Netherlands

    Peter van Emde Boas

  3. Dept. Comp. Sci., University of Petroleum, Chang Ping, Beijing, P.R. China

    Peter van Emde Boas

Authors
  1. Peter van Emde Boas
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Editor information

Editors and Affiliations

  1. Faculty of Informatics and Information Technologies, Institute of Informatics and Software Engineering, Slovak University of Technology in Bratislava, Ilkovičova 3, 842 16, Bratislava 4, Slovakia

    Mária Bieliková

  2. Dept. of Intelligent Systems and Business Informatics, Alpen-Adria-Universität Klagenfurt, Universitätsstr. 65-57, 9020, Klagenfurt, Austria

    Gerhard Friedrich

  3. Department of Computer Science, University of Oxford, UK

    Georg Gottlob

  4. Security Engineering Group, Technische Universität Darmstadt, Hochschulstr. 10, 64289, Darmstadt, Germany

    Stefan Katzenbeisser

  5. University of Illinois at Chicago, Dept. of Math., Stat. and Comp. Sci, 851 S. Morgan Street, Chicago, IL 60607-7045, USA; and University of Szeged, Research Group on Artificial Intelligence of the Hungarian Academy of Sciences, 6701 Szeged, Postafiók, Hungary

    György Turán

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© 2012 Springer-Verlag Berlin Heidelberg

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van Emde Boas, P. (2012). Turing Machines for Dummies. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds) SOFSEM 2012: Theory and Practice of Computer Science. SOFSEM 2012. Lecture Notes in Computer Science, vol 7147. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27660-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-27660-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27659-0

  • Online ISBN: 978-3-642-27660-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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