Skip to main content
SpringerLink
Log in

A Universal Oracle for Signal Machines

  • Conference paper
  • First Online:
Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

Included in the following conference series:

  • 607 Accesses

Abstract

We construct two universal oracles for signal machines, one via the binary expansion of irrational numbers, another via their continued fraction expansion, settling a conjecture of Durand-Lose in CiE 2013. This latter is optimal in the number of speeds and irrational parameters involved in the construction (three and one respectively).

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 EPUB and 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

References

  1. 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. Am. Math. Soc. New Ser. 21(1), 1–46 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Durand-Lose, J.: Calculer géométriquement sur le plan - machines à signaux. Habilitation à Diriger des Recherches, École Doctorale STIC, Université de Nice-Sophia Antipolis (2003) (In French)

    Google Scholar 

  3. Durand-Lose, J.: Abstract geometrical computation and the linear Blum, Shub and Smale model. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) CiE 2007. LNCS, vol. 4497, pp. 238–247. Springer, Heidelberg (2007). doi:10.1007/978-3-540-73001-9_25

    Chapter  Google Scholar 

  4. Durand-Lose, J.: Abstract geometrical computation 3: black holes for classical and analog computing. Nat. Comput. 8(3), 455–472 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Durand-Lose, J.: Irrationality is needed to compute with signal machines with only three speeds. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 108–119. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39053-1_12

    Chapter  Google Scholar 

  6. Khinchin, A.I.A., Eagle, H.: Continued Fractions. Dover Books on Mathematics. Dover Publications, New York (1964)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS – LIPN – Université Paris 13, Villetaneuse, France

    Thierry Monteil

Authors
  1. Thierry Monteil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thierry Monteil .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Monteil, T. (2017). A Universal Oracle for Signal Machines. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-58741-7_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation