Squeezing Feasibility

  • Walter Dean
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9709)


This note explores an often overlooked question about the characterization of the notion model of computation which was originally identified by Cobham [5]. A simple formulation is as follows: what primitive operations are allowable in the definition of a model such that its time and space complexity measures provide accurate gauges of practical computational difficulty? After exploring the significance of this question in the context of subsequent work on machine models and simulations, an adaptation of Kreisel’s squeezing argument [17] for Church’s Thesis involving Gandy machines [11] is sketched which potentially bears on this question.


Polynomial Time Turing Machine Computable Function Polynomial Space Primitive Operation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Arora, S., Barak, B.: Computational Complexity: A Modern Approach. University Press, Cambridge (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bertoni, A., Mauri, G., Sabadini, N.: Simulations among classes of random access machines and equivalence among numbers succinctly represented. In: Annals of Discrete Mathematics. North-Holland Mathematics Studies, vol. 109, pp. 65–89. Elsevier (1985)Google Scholar
  3. 3.
    Buss, R.: Bounded Arithmetic. Bibliopolis, Naples (1986)zbMATHGoogle Scholar
  4. 4.
    Clote, P.: Boolean Functions and Computation Models. Springer, Heidelberg (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Cobham, A.: The intrinsic computational difficulty of functions. In: Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, Amsterdam, pp. 24–30. North-Holland (1965)Google Scholar
  6. 6.
    Cook, S.: An overview of computational complexity. Commun. ACM 26, 401–408 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cook, S., Aanderaa, S.: On the minimum computation time of functions. Trans. Am. Math. Soc. 142, 291–314 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Cook, S., Reckhow, R.: Time bounded random access machines. J. Comput. Syst. Sci. 7(4), 354–375 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dean, W.: Computational complexity theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Fall 2015 Ed. (2015)Google Scholar
  10. 10.
    Fürer, M.: Faster integer multiplication. SIAM J. Comput. 39(3), 979–1005 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gandy, R.: Church’s thesis and principles for mechanisms. In: Barwise, H.K.J., Kunen, K. (eds.) The Kleene Symposium, vol. 101, pp. 123–148. North Holland, Amsterdam (1980)CrossRefGoogle Scholar
  12. 12.
    Hartmanis, J., Simon, J.: On the power of multiplication in random access machines. In: 1974 IEEE Conference Record of 15th Annual Symposium on Switching and Automata Theory, pp. 13–23. IEEE (1974)Google Scholar
  13. 13.
    Hartmanis, J., Stearns, R.: On the computational complexity of algorithms. Trans. Am. Math. Soc. 117(5), 285–306 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Immerman, N.: Descriptive Complexity. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  15. 15.
    Knuth, D.: The Art of Computer Programming, vol. I–III. Addison Wesley, Boston (1973)Google Scholar
  16. 16.
    Kolmogorov, A., Uspensky, V.: To the definition of algorithms. Uspekhi Mat. Nauk 13(4), 3–28 (1958)Google Scholar
  17. 17.
    Kreisel, G.: Informal rigour and completeness proofs. In: Problems in the Philosophy of Mathematics, pp. 138–186 (1967)Google Scholar
  18. 18.
    Kreisel, G.: Which number theoretic problems can be solved in recursive progressions on \(\Pi ^1_1\)-paths through \(\cal {O}\)? J. Symbolic Logic 37(2), 311–334 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kreisel, G.: Church’s thesis and the ideal of informal rigour. Notre Dame J. Formal Logic 28(4), 499–519 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Rose, H.: Subrecursion: Functions and Hierarchies. Clarendon Press, Oxford (1984)zbMATHGoogle Scholar
  21. 21.
    Savitch, W., Stimson, M.: Time bounded random access machines with parallel processing. J. ACM 26(1), 103–118 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Schönhage, A.: Storage modification machines. SIAM J. Comput. 9(3), 490–508 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7(3–4), 281–292 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Sieg, W.: On computability. In: Irvine, A. (ed.) Philosophy of Mathematics, Handbook of the Philosophy of Science, vol. 4, pp. 549–630. North Holland, Amsterdam (2009)Google Scholar
  25. 25.
    Turing, A.: On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 42(2), 230–265 (1936)MathSciNetzbMATHGoogle Scholar
  26. 26.
    van Emde Boas, P.: Space measures for storage modification machines. Inf. Process. Lett. 30(2), 103–110 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    van Emde Boas, P.: Machine models and simulations. In: Van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science (vol. A): Algorithms and Complexity. MIT Press, Cambridge (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of WarwickCoventryUK

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