Skip to main content
SpringerLink
Log in

Towards an Axiomatization of Simple Analog Algorithms

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7287))

Abstract

We propose a formalization of analog algorithms, extending the framework of abstract state machines to continuous-time models of computation.

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

Access this chapter

Log in via an institution
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.

Similar content being viewed by others

References

  1. Wikipedia. MONIAC computer, http://en.wikipedia.org/wiki/MONIAC_Computer (viewed March 1, 2012)

  2. Blass, A., Dershowitz, N., Gurevich, Y.: Exact Exploration and Hanging Algorithms. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 140–154. Springer, Heidelberg (2010), http://nachum.org/papers/HangingAlgorithms.pdf (viewed May 27, 2011)

    Chapter  Google Scholar 

  3. Blum, L., Shub, M., Smale, S.: On a theory of computation and complexity over the real numbers: NP completeness, recursive functions and universal machines. Bull. Amer. Math. Soc. (NS) 21, 1–46 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Boker, U., Dershowitz, N.: The Church-Turing Thesis over Arbitrary Domains. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 199–229. Springer, Heidelberg (2008), http://nachum.org/papers/ArbitraryDomains.pdf (viewed January 10, 2012)

    Chapter  Google Scholar 

  5. Boker, U., Dershowitz, N.: Three Paths to Effectiveness. In: Blass, A., Dershowitz, N., Reisig, W. (eds.) Fields of Logic and Computation. LNCS, vol. 6300, pp. 135–146. Springer, Heidelberg (2010), http://nachum.org/papers/ThreePathsToEffectiveness.pdf (viewed January 10, 2012)

    Chapter  Google Scholar 

  6. Bush, V.: The differential analyser. Journal of the Franklin Institute 212(4), 447–488 (1931)

    Article  Google Scholar 

  7. Bournez, O., Campagnolo, M.L.: A survey on continuous time computations. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) New Computational Paradigms Changing Conceptions of What is Computable, pp. 383–423. Springer, New York (2008)

    Google Scholar 

  8. Cohen, J., Slissenko, A.: On implementations of instantaneous actions real-time ASM by ASM with delays. In: Proc. of the 12th Intern. Workshop on Abstract State Machines (ASM 2005), Paris, France, pp. 387–396 (2005)

    Google Scholar 

  9. Cohen, J., Slissenko, A.: Implementation of sturdy real-time abstract state machines by machines with delays. In: Proc. of the 6th Intern. Conf. on Computer Science and Information Technology (CSIT 2007). Academy of Science of Armenia, Yerevan (2007)

    Google Scholar 

  10. Coward, D.: Doug Coward’s Analog Computer Museum (2006), http://www.cowardstereoview.com/analog/ (viewed January 10, 2012)

  11. Dershowitz, N., Falkovich, E.: A formalization and proof of the Extended Church-Turing Thesis (extended abstract). In: Studia Logica Conference on Trends in Logic, IX: Church Thesis: Logic, Mind and Nature, Krakow, Poland (June 2011), http://nachum.org/papers/ECTT.pdf (viewed January 10, 2012)

  12. Dershowitz, N., Gurevich, Y.: A natural axiomatization of computability and proof of Church’s Thesis. The Bulletin of Symbolic Logic 14(3), 299–350 (2009), http://nachum.org/papers/Church.pdf (viewed April 15, 2009)

    MathSciNet  Google Scholar 

  13. Glausch, A., Reisig, W.: A Semantic Characterization of Unbounded-Nondeterministic Abstract State Machines. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 242–256. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Gurevich, Y.: Evolving algebras 1993: Lipari guide. In: Börger, E. (ed.) Specification and Validation Methods, pp. 9–36. Oxford University Press (1995), http://research.microsoft.com/~gurevich/opera/103.pdf (viewed April 15, 2009)

  15. Gurevich, Y.: Sequential abstract-state machines capture sequential algorithms. ACM Transactions on Computational Logic 1, 77–111 (2000), http://research.microsoft.com/~gurevich/opera/141.pdf (viewed April 15, 2009)

    Article  MathSciNet  Google Scholar 

  16. Gurevich, Y., Yavorskaya, T.: On bounded exploration and bounded nondeterminism. Technical Report MSR-TR-2006-07, Microsoft Research, Redmond, WA (January 2006), http://research.microsoft.com/~gurevich/opera/177.pdf (viewed January 10, 2012)

  17. Reisig, W.: On Gurevich’s theorem on sequential algorithms. Acta Informatica 39(5), 273–305 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rust, H.: Hybrid abstract state machines: Using the hyperreals for describing continuous changes in a discrete notation. In: Gurevich, Y., Kutter, P., Odersky, M., Thiele, L. (eds.) International Workshop on Abstract State Machines (Monte Verita, Switzerland), TIK-Report 87, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland, pp. 341–356 (March 2000)

    Google Scholar 

  19. Shannon, C.E.: Mathematical theory of the differential analyser. Journal of Mathematics and Physics 20, 337–354 (1941)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIX, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Olivier Bournez

  2. School of Computer Science, Tel Aviv University, Ramat Aviv, 69978, Israel

    Nachum Dershowitz & Evgenia Falkovich

Authors
  1. Olivier Bournez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nachum Dershowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evgenia Falkovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Resource Planning and Generation, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Manindra Agrawal

  2. Department of Pure Mathematics, Leeds, University of Leeds, LS2 9JT, UK

    S. Barry Cooper

  3. Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, 100190, Beijing, P.R. China

    Angsheng Li

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bournez, O., Dershowitz, N., Falkovich, E. (2012). Towards an Axiomatization of Simple Analog Algorithms. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29952-0_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29951-3

  • Online ISBN: 978-3-642-29952-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation