Skip to main content

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

Abstract

We attempt to put the title problem and the Church-Turing thesis into a proper perspective and to clarify some common misconceptions related to Turing’s analysis of computation. We examine two approaches to the title problem, one well-known among philosophers and another among logicians.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abiteboul, S., Vianu, V.: Datalog extensions for database queries and updates. J. of Computer and System Sciences 43, 62–124 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Biedl, T., Buss, J.F., Demaine, E.D., Demaine, M.L., Hajiaghayi, M., Vinař, T.: Palindrome recognition using a multidemensional tape. Theoretical Computer Science 302, 475–480 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blass, A., Gurevich, Y.: Abstract state machines capture parallel algorithms. ACM Transactions on Computational Logic 4(4), 578–651 (2003); Correction and extension, same journal 9(3) article 19 (2008)

    Google Scholar 

  4. Blass, A., Gurevich, Y.: Algorithms vs. machines. Bull. European Association for Theoretical Computer Science 77, 96–118 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Blass, A., Gurevich, Y.: Algorithms: A quest for absolute definitions. In: Current Trends in Theoretical Computer Science, pp. 195–225. World Scientific (2004); also in Olszewski, A., et al. (eds): Church’s Thesis after 70 Years, pp. 24–57. Ontos Verlag (2006)

    Google Scholar 

  6. Blass, A., Gurevich, Y.: Ordinary interactive small-step algorithms. ACM Trans. Computational Logic (Part I), 7(2), 363–419 (2006); plus 8(3), articles 15 and 16 (Parts II, III) (2007)

    Google Scholar 

  7. Blass, A., Gurevich, Y., Rosenzweig, D., Rossman, B.: Interactive small-step algorithms. Logical Methods in Computer Science 3(4), papers 3 and 4 (Part I and Part II) (2007)

    Google Scholar 

  8. Dershowitz, N., Gurevich, Y.: A natural axiomatization of computability and proof of Church’s thesis. Bull. of Symbolic Logic 14(3), 299–350 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gandy, R.: Church’s thesis and principles for mechanisms. In: Barwise, J., et al. (eds.) The Kleene Symposium, pp. 123–148. North-Holland (1980)

    Google Scholar 

  10. Cooper, S., Löwe, B., Sorbi, A. (eds.): New Computational Paradigms: Changing Conceptions of what is Computable. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  11. Grädel, E., Nowack, A.: Quantum Computing and Abstract State Machines. In: Börger, E., Gargantini, A., Riccobene, E. (eds.) ASM 2003. LNCS, vol. 2589, pp. 309–323. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Gurevich, Y.: Sequential Abstract State Machines Capture Sequential Algorithms. ACM Transactions on Computational Logic 1(1), 77–111 (2000)

    Article  MathSciNet  Google Scholar 

  13. Gurevich, Y., Shelah, S.: Fixed-point extensions of first-order logic. Annals of Pure and Applied Logic 32, 265–280 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  14. Kolmogorov, A.N.: On the concept of algorithm. Uspekhi Mat. Nauk 8(4), 175–176 (1953) (in Russian); English translation in [25]

    Google Scholar 

  15. McCarthy, J.: A basis for a mathematical theory of computation. In: Brafford, P., Herschberg, D. (eds.) Computer Programming and Formal Systems, pp. 33–70. North-Holland (1963)

    Google Scholar 

  16. Moschovakis, Y.N.: Abstract recursion as a foundation of the theory of algorithms. In: Computation and Proof Theory. Lecture Notes in Mathematics, vol. 1104, pp. 289–364. Springer, Heidelberg (1984)

    Chapter  Google Scholar 

  17. Moschovakis, Y.N.: What is an algorithm? In: Engquist, B., Schmid, W. (eds.) Mathematics Unlimited – 2001 and Beyond, pp. 919–936. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  18. Moschovakis, Y.N.: Algorithms and implementations. Tarski Lecture 1 (2008), http://www.math.ucla.edu/~ynm/lectures/tlect1.pdf

  19. Moschovakis, Y.N., Paschalis, V.: Elementary algorithms and their implementations. In: [10], pp. 87–118

    Google Scholar 

  20. Shagrir, O.: Effective computation by humans and machines. Minds and Machines 12, 221–240 (2002)

    Article  MATH  Google Scholar 

  21. Sieg, W.: Calculations by man & machine: Mathematical presentation. In: Proceedings of the Cracow International Congress of Logic, Methodology and Philosophy of Science, pp. 245–260. Kluwer (2002)

    Google Scholar 

  22. Sieg, W.: Church without dogma – Axioms for computability. In: [10], pp. 139–152

    Google Scholar 

  23. Sieg, W.: On Computability. In: Irvine, A. (ed.) Handbook of the Philosophy of Mathematics, pp. 535–630. Elsevier (2009)

    Google Scholar 

  24. Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proceedings of London Mathematical Society, Series 2 42, 230–265 (1936-1937); Correction, same journal 43, 544–546

    Google Scholar 

  25. Uspensky, V.A., Semenov, A.L.: Algorithms: Main Ideas and Applications. Kluwer (1993)

    Google Scholar 

  26. Valarcher, P.: Habilitation à Diriger des Recherches, Université Paris Est Créteil, LACL (EA 4219), Département d’Informatique, IUT Fontainebleau, France (2010), http://www.paincourt.net/perso/Publi/hdr.pdf

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gurevich, Y. (2012). What Is an Algorithm?. 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_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-27660-6_3

  • 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)

Publish with us

Policies and ethics